Math @ Duke
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Books
- R.T. Durrett, Branching process models of cancer
(2015), Springer
- R. Durrett, Probability: Theory and Examples, 4th Edition
(2010), Cambridge U Press
- R. Durrett, Elementary Probability for Applications, 4th Edition
(2009),
pp. x+243, Cambridge University Press, Cambridge, ISBN 978-0-521-86756-6 [MR2537423 (2010i:60003)]
- R. Durrett, Probability Models of DNA Sequence Evolution, 2nd Edition
(2006), Springer
- R. Durrett, Essentials of Stochastic Processes
(1998), Springer-Verlag
- R. Durrett, Stochastic Calculus: A Practrical Introduction
(1996), CRC Press
- R. Durrett, Lecture Notes on Particle Systems and Percolation
(1988), Wadsworth
- R. Durrett, Brownian Motion and Martingales in Analysis
(1984), Wadsworth
Papers Published
- Huang, X; Durrett, R, Corrigendum to: The contact process on periodic trees (Electronic Communications in Probability),
Electronic Communications in Probability, vol. 28
(January, 2023) [doi] [abs]
- Tung, H-R; Durrett, R, Competitive exclusion in a model with seasonality: Three species cannot coexist in an ecosystem with two seasons.,
Theoretical population biology, vol. 148
(December, 2022),
pp. 40-45 [doi] [abs]
- Boyle, L; Hletko, S; Huang, J; Lee, J; Pallod, G; Tung, H-R; Durrett, R, Selective sweeps in SARS-CoV-2 variant competition.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 119 no. 47
(November, 2022),
pp. e2213879119 [doi] [abs]
- Durrett, R; Yao, D, Susceptible–infected epidemics on evolving graphs,
Electronic Journal of Probability, vol. 27
(January, 2022),
pp. 1-66 [doi] [abs]
- Huang, X; Durrett, R, Motion by mean curvature in interacting particle systems,
Probability Theory and Related Fields, vol. 181 no. 1-3
(November, 2021),
pp. 489-532 [doi] [abs]
- Durrett, RT, Mathematical modeling in ecology, genetics and cancer research,
in The Art And Practice Of Mathematics: Interviews At The Institute For Mathematical Sciences, National University Of Singapore, 2010-2020
(June, 2021),
pp. 74-82, ISBN 9789811219580
- Tung, H-R; Durrett, R, Signatures of neutral evolution in exponentially growing tumors: A theoretical perspective.,
PLoS computational biology, vol. 17 no. 2
(February, 2021),
pp. e1008701 [doi] [abs]
- Agarwal, P; Simper, M; Durrett, R, The q-voter model on the torus,
Electronic Journal of Probability, vol. 26
(January, 2021) [doi] [abs]
- Borowiak, M; Ning, F; Pei, J; Zhao, S; Tung, H-R; Durrett, R, Controlling the spread of COVID-19 on college campuses.,
Mathematical biosciences and engineering : MBE, vol. 18 no. 1
(December, 2020),
pp. 551-563 [doi] [abs]
- Cristali, I; Junge, M; Durrett, R, Poisson percolation on the oriented square lattice,
Stochastic Processes and their Applications, vol. 130 no. 2
(February, 2020),
pp. 488-502 [doi] [abs]
- Huang, X; Durrett, R, The contact process on periodic trees,
Electronic Communications in Probability, vol. 25
(January, 2020) [doi] [abs]
- Durrett, R; Junge, M; Tang, S, Coexistence in chase-escape,
Electronic Communications in Probability, vol. 25
(January, 2020) [doi] [abs]
- Huang, X; Durrett, R, The contact process on random graphs and Galton Watson trees,
Alea (Rio de Janeiro), vol. 17 no. 1
(January, 2020),
pp. 159-182 [doi] [abs]
- Durrett, R; Yao, D, The symbiotic contact process,
Electronic Journal of Probability, vol. 25
(January, 2020) [doi] [abs]
- Wang, Z; Durrett, R, Extrapolating weak selection in evolutionary games.,
Journal of mathematical biology, vol. 78 no. 1-2
(January, 2019),
pp. 135-154 [doi] [abs]
- Huo, R; Durrett, R, The Zealot voter model,
Annals of Applied Probability, vol. 29 no. 5
(January, 2019),
pp. 3128-3154 [doi] [abs]
- Ma, R; Durrett, R, A simple evolutionary game arising from the study of the role of igf-II in pancreatic cancer,
Annals of Applied Probability, vol. 28 no. 5
(October, 2018),
pp. 2896-2921, Institute of Mathematical Statistics [doi] [abs]
- Talkington, A; Dantoin, C; Durrett, R, Ordinary Differential Equation Models for Adoptive Immunotherapy.,
Bulletin of mathematical biology, vol. 80 no. 5
(May, 2018),
pp. 1059-1083 [doi] [abs]
- Huo, R; Durrett, R, Latent voter model on locally tree-like random graphs,
Stochastic Processes and their Applications, vol. 128 no. 5
(May, 2018),
pp. 1590-1614, Elsevier BV [doi] [abs]
- Beckman, E; Dinan, E; Durrett, R; Huo, R; Junge, M, Asymptotic behavior of the brownian frog model,
Electronic Journal of Probability, vol. 23
(January, 2018), Institute of Mathematical Statistics [doi] [abs]
- Basak, A; Durrett, R; Foxall, E, Diffusion limit for the partner model at the critical value,
Electronic Journal of Probability, vol. 23
(January, 2018), Institute of Mathematical Statistics [doi] [abs]
- Nolen, JH; Cristali, I; Ranjan, V; Steinberg, J; Beckman, E; Durrett, R; Junge, M, Block size in Geometric(p)-biased permutations,
Electronic Communications in Probability, vol. 23
(2018),
pp. 1-10, Institute of Mathematical Statistics [doi] [abs]
- Lopatkin, AJ; Meredith, HR; Srimani, JK; Pfeiffer, C; Durrett, R; You, L, Persistence and reversal of plasmid-mediated antibiotic resistance.,
Nature communications, vol. 8 no. 1
(November, 2017),
pp. 1689 [doi] [abs]
- Gleeson, JP; Durrett, R, Temporal profiles of avalanches on networks.,
Nature communications, vol. 8 no. 1
(October, 2017),
pp. 1227 [doi] [abs]
- Tomasetti, C; Durrett, R; Kimmel, M; Lambert, A; Parmigiani, G; Zauber, A; Vogelstein, B, Role of stem-cell divisions in cancer risk.,
Nature, vol. 548 no. 7666
(August, 2017),
pp. E13-E14, Springer Nature [doi]
- Bessonov, M; Durrett, R, Phase transitions for a planar quadratic contact process,
Advances in Applied Mathematics, vol. 87
(June, 2017),
pp. 82-107, Elsevier BV [doi] [abs]
- Nanda, M; Durrett, R, Spatial evolutionary games with weak selection.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 114 no. 23
(June, 2017),
pp. 6046-6051 [doi] [abs]
- Durrett, R; Fan, WTL, Genealogies in expanding populations,
Annals of Applied Probability, vol. 26 no. 6
(December, 2016),
pp. 3456-3490, Institute of Mathematical Statistics [doi] [abs]
- Ryser, MD; Worni, M; Turner, EL; Marks, JR; Durrett, R; Hwang, ES, Outcomes of Active Surveillance for Ductal Carcinoma in Situ: A Computational Risk Analysis.,
J Natl Cancer Inst, vol. 108 no. 5
(May, 2016),
pp. djv372 [doi] [abs]
- Durrett, R; Foo, J; Leder, K, Spatial Moran models, II: cancer initiation in spatially structured tissue.,
Journal of mathematical biology, vol. 72 no. 5
(April, 2016),
pp. 1369-1400, ISSN 0303-6812 [doi] [abs]
- Cox, JT; Durrett, R, Evolutionary games on the torus with weak selection,
Stochastic Processes and their Applications, vol. 126 no. 8
(December, 2015),
pp. 2388-2409, Elsevier BV [doi] [abs]
- Durrett, R; Zhang, Y, Coexistence of grass, saplings and trees in the Staver-Levin forest model,
Annals of Applied Probability, vol. 25 no. 6
(December, 2015),
pp. 3434-3464, Institute of Mathematical Statistics, ISSN 1050-5164 [doi] [abs]
- Talkington, A; Durrett, R, Estimating Tumor Growth Rates In Vivo.,
Bulletin of mathematical biology, vol. 77 no. 10
(October, 2015),
pp. 1934-1954, ISSN 0092-8240 [doi] [abs]
- Varghese, C; Durrett, R, Spatial networks evolving to reduce length,
Journal of Complex Networks, vol. 3 no. 3
(September, 2015),
pp. 411-430, Oxford University Press (OUP) [doi] [abs]
- Ryser, MD; Myers, ER; Durrett, R, HPV clearance and the neglected role of stochasticity.,
PLoS Comput Biol, vol. 11 no. 3
(March, 2015),
pp. e1004113, Public Library of Science, ISSN 1553-734X [repository], [doi] [abs]
- Durrett, R; Moseley, S, Spatial moran models I. Stochastic tunneling in the neutral case,
Annals of Applied Probability, vol. 25 no. 1
(February, 2015),
pp. 104-115, Institute of Mathematical Statistics, ISSN 1050-5164 [doi] [abs]
- Magura, SR; Pong, VH; Durrett, R; Sivakoff, D, Two evolving social network models,
Alea, vol. 12 no. 2
(January, 2015),
pp. 699-715 [abs]
- Durrett, R, Spatial evolutionary games with small selection coefficients,
Electronic Journal of Probability, vol. 19
(December, 2014), Institute of Mathematical Statistics [doi] [abs]
- Aristotelous, AC; Durrett, R, Fingering in stochastic growth models,
Experimental Mathematics, vol. 23 no. 4
(October, 2014),
pp. 465-474, Informa UK Limited, ISSN 1058-6458 [doi] [abs]
- Durrett, R; Zhang, Y, Exact solution for a metapopulation version of Schelling's model.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 111 no. 39
(September, 2014),
pp. 14036-14041, ISSN 0027-8424 [doi] [abs]
- Aristotelous, AC; Durrett, R, Chemical evolutionary games.,
Theoretical population biology, vol. 93
(May, 2014),
pp. 1-13, ISSN 0040-5809 [doi] [abs]
- Durrett, R; Liggett, T; Zhang, Y, The contact process with fast voting,
Electronic Journal of Probability, vol. 19
(March, 2014), Institute of Mathematical Statistics [doi] [abs]
- Shi, F; Mucha, PJ; Durrett, R, Multiopinion coevolving voter model with infinitely many phase transitions.,
Physical review. E, Statistical, nonlinear, and soft matter physics, vol. 88 no. 6
(December, 2013),
pp. 062818, ISSN 1539-3755 [doi] [abs]
- Varghese, C; Durrett, R, Phase transitions in the quadratic contact process on complex networks,
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 87 no. 6
(June, 2013),
pp. paper 062819, American Physical Society (APS), ISSN 1539-3755 [doi] [abs]
- Mode, CJ; Durrett, R; Klebaner, F; Olofsson, P, Applications of stochastic processes in biology and medicine,
International Journal of Stochastic Analysis, vol. 2013
(April, 2013),
pp. 1-2, Hindawi Limited, ISSN 2090-3332 [doi]
- Durrett, R, Cancer modeling: A personal perspective,
Notices of the American Mathematical Society, vol. 60 no. 3
(March, 2013),
pp. 304-309, American Mathematical Society (AMS), ISSN 0002-9920 [doi]
- Danesh, K; Durrett, R; Havrilesky, LJ; Myers, E, A branching process model of ovarian cancer.,
J Theor Biol, vol. 314
(December, 2012),
pp. 10-15 [22959913], [doi] [abs]
- Durrett, R; Remenik, D, Evolution of dispersal distance.,
Journal of mathematical biology, vol. 64 no. 4
(March, 2012),
pp. 657-666, ISSN 0303-6812 [doi] [abs]
- Durrett, R; Gleeson, JP; Lloyd, AL; Mucha, PJ; Shi, F; Sivakoff, D; Socolar, JES; Varghese, C, Graph fission in an evolving voter model.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 109 no. 10
(March, 2012),
pp. 3682-3687 [22355142], [doi] [abs]
- Durrett, R; Chatterjee, S, A first order phase transition in the threshold theta contact process on random r-regular graphs and trees,
Stoch. Proc. Appl., vol. 123 no. 2
(2012),
pp. 561-578, Elsevier BV [doi] [abs]
- Chatterjee, S; Durrett, R, Asymptotic behavior of Aldous' gossip process,
Annals of Applied Probability, vol. 21 no. 6
(December, 2011),
pp. 2447-2482, Institute of Mathematical Statistics, ISSN 1050-5164 [math.PR/1005.1608], [doi] [abs]
- Chatterjee, S; Durrett, R, Persistence of activity in threshold contact processes, an "Annealed approximation" of random Boolean networks,
Random Structures and Algorithms, vol. 39 no. 2
(September, 2011),
pp. 228-246, WILEY, ISSN 1042-9832 [MR2850270], [doi] [abs]
- Durrett, R; Foo, J; Leder, K; Mayberry, J; Michor, F, Intratumor heterogeneity in evolutionary models of tumor progression.,
Genetics, vol. 188 no. 2
(June, 2011),
pp. 461-477, ISSN 0016-6731 [doi] [abs]
- Durrett, R; Mayberry, J, Traveling waves of selective sweeps,
Annals of Applied Probability, vol. 21 no. 2
(April, 2011),
pp. 699-744, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2807971], [doi] [abs]
- Durrett, R; Remenik, D, Brunet-derrida particle systems, free boundary problems and wiener-hopf equations,
Annals of Probability, vol. 39 no. 6
(January, 2011),
pp. 2043-2078, Institute of Mathematical Statistics, ISSN 0091-1798 [doi] [abs]
- Durrett, R, Population genetics of neutral mutations in exponentially growing cancer cell populations,
Annals of Applied Probability, vol. 23 no. 1
(2011),
pp. 230-250, Institute of Mathematical Statistics [doi] [abs]
- Cox, JT; Durrett, R; Perkins, E, Voter model perturbations and reaction diffusion equations,
Asterique, vol. 349 no. 349
(2011),
pp. 1-127 [math.PR/1103.1676] [abs]
- Durrett, R; Chatterjee, S, Persistence of activity in random Boolean networks,
Random Structures and Algorithms, vol. 39
(2011),
pp. 228-246
- Durrett, R; Foo, J; Leder, K; Mayberry, J; Michor, F, Evolutionary dynamics of tumor progression with random fitness values.,
Theoretical population biology, vol. 78 no. 1
(August, 2010),
pp. 54-66, ISSN 0040-5809 [math.PR/1003.1927], [doi] [abs]
- Durrett, R; Mayberry, J, Evolution in predator-prey systems,
Stochastic Processes and their Applications, vol. 120 no. 7
(July, 2010),
pp. 1364-1392, Elsevier BV, ISSN 0304-4149 [MR2011d:92087], [doi] [abs]
- Durrett, R, Some features of the spread of epidemics and information on a random graph.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 107 no. 10
(March, 2010),
pp. 4491-4498, ISSN 0027-8424 [doi] [abs]
- Durrett, R; Moseley, S, Evolution of resistance and progression to disease during clonal expansion of cancer.,
Theoretical population biology, vol. 77 no. 1
(February, 2010),
pp. 42-48, ISSN 0040-5809 [doi] [abs]
- Chatterjee, S; Durrett, R, Contact processes on random graphs with power law degree distributions have critical value 0,
Annals of Probability, vol. 37 no. 6
(November, 2009),
pp. 2332-2356, Institute of Mathematical Statistics, ISSN 0091-1798 [doi] [abs]
- Chan, B; Durrett, R; Lanchier, N, Coexistence for a multitype contact process with seasons,
Annals of Applied Probability, vol. 19 no. 5
(October, 2009),
pp. 1921-1943, Institute of Mathematical Statistics, ISSN 1050-5164 [doi] [abs]
- Durrett, R; Remenik, D, Chaos in a spatial epidemic model,
Annals of Applied Probability, vol. 19 no. 4
(August, 2009),
pp. 1656-1685, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2010k:60322], [doi] [abs]
- Wu, F; Eannetta, NT; Xu, Y; Durrett, R; Mazourek, M; Jahn, MM; Tanksley, SD, A COSII genetic map of the pepper genome provides a detailed picture of synteny with tomato and new insights into recent chromosome evolution in the genus Capsicum.,
TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik, vol. 118 no. 7
(May, 2009),
pp. 1279-1293, ISSN 0040-5752 [doi] [abs]
- Durrett, R, SPecial invited paper coexistence in stochastic spatial models,
Annals of Applied Probability, vol. 19 no. 2
(April, 2009),
pp. 477-496, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2521876 (2010g:60213)], [doi] [abs]
- Durrett, R; Schmidt, D; Schweinsberg, J, A waiting time problem arising from the study of multi-stage carcinogenesis,
Annals of Applied Probability, vol. 19 no. 2
(April, 2009),
pp. 676-718, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2521885 (2010f:60243)], [doi] [abs]
- Durrett, R; Schmidt, D, Reply to Michael Behe,
Genetics, vol. 181 no. 2
(February, 2009),
pp. 821-822, Genetics Society of America, ISSN 0016-6731 [doi]
- Durrett, R; Popovic, L, Degenerate diffusions arising from gene duplication models,
Annals of Applied Probability, vol. 19 no. 1
(February, 2009),
pp. 15-48, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2521876 (2010g:60213)], [doi] [abs]
- Chan, B; Durrett, R; Lanchier, N, Coexistence in a particle system with seasons,
Ann. Appl. Probab., vol. 19 no. 5
(2009),
pp. 1921-1943, ISSN 1050-5164 [doi] [abs]
- Durrett, R; Schmidt, D, Waiting for two mutations: with applications to regulatory sequence evolution and the limits of Darwinian evolution.,
Genetics, vol. 180 no. 3
(November, 2008),
pp. 1501-1509, ISSN 0016-6731 [doi] [abs]
- Durrett, R; Lanchier, N, Coexistence in host-pathogen systems,
Stochastic Processes and their Applications, vol. 118 no. 6
(June, 2008),
pp. 1004-1021, Elsevier BV, ISSN 0304-4149 [MR2418255 (2009g:60131)], [doi] [abs]
- Durrett, R; Restrepo, M, One-dimensional stepping stone models, sardine genetics and Brownian local time,
Annals of Applied Probability, vol. 18 no. 1
(February, 2008),
pp. 334-358, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2380901 (2008j:60229)], [doi] [abs]
- Huerta-Sanchez, E; Durrett, R; Bustamante, CD, Population genetics of polymorphism and divergence under fluctuating selection.,
Genetics, vol. 178 no. 1
(January, 2008),
pp. 325-337, ISSN 0016-6731 [doi] [abs]
- Berestycki, N; Durrett, R, Limiting behavior for the distance of a random walk,
Electronic Journal of Probability, vol. 13
(January, 2008),
pp. 374-395, Institute of Mathematical Statistics, ISSN 1083-6489 [MR2386737 (2009d:60130)], [doi] [abs]
- Chung, KL; Durrett, R, Downcrossings and local time,
in Selected Works of Kai Lai Chung
(January, 2008),
pp. 585-587, World Scientific, ISBN 9789812833853 [doi] [abs]
- Durrett, R; Zähle, I, On the width of hybrid zones,
Stochastic Processes and their Applications, vol. 117 no. 12
(December, 2007),
pp. 1751-1763, Elsevier BV, ISSN 0304-4149 [MR2437727 (2010d:60215)], [doi] [abs]
- Durrett, R; Jung, P, Two phase transitions for the contact process on small worlds,
Stochastic Processes and their Applications, vol. 117 no. 12
(December, 2007),
pp. 1910-1927, Elsevier BV, ISSN 0304-4149 [MR2437735 (2009h:60162)], [doi] [abs]
- Sainudiin, R; Clark, AG; Durrett, RT, Simple models of genomic variation in human SNP density.,
BMC genomics, vol. 8
(June, 2007),
pp. 146, ISSN 1471-2164 (paper 146.) [doi] [abs]
- De, A; Durrett, R, Stepping-stone spatial structure causes slow decay of linkage disequilibrium and shifts the site frequency spectrum.,
Genetics, vol. 176 no. 2
(June, 2007),
pp. 969-981, ISSN 0016-6731 [doi] [abs]
- York, TL; Durrett, R; Nielsen, R, Dependence of paracentric inversion rate on tract length.,
BMC bioinformatics, vol. 8
(April, 2007),
pp. 115, ISSN 1471-2105 (paper 115.) [doi] [abs]
- Huerta-Sanchez, E; Durrett, R, Wagner's canalization model.,
Theoretical population biology, vol. 71 no. 2
(March, 2007),
pp. 121-130, ISSN 0040-5809 [doi] [abs]
- Durrett, R; Schmidt, D, Waiting for regulatory sequences to appear,
Annals of Applied Probability, vol. 17 no. 1
(February, 2007),
pp. 1-32, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2292578 (2007j:92034)], [doi] [abs]
- R. Durrett and Iljana Zahle, On the width of hybrid zones,
Stochastic Processes and their Applications, vol. 117
(2007),
pp. 1751--1763, ISSN 0304-4149 [MR2010d:60215]
- De, A; Durrett, R, Spatial structure of the human population contributes to the slow decay of linkage diseqeuilibrium and shifts the site frequency spectrum,
Genetics, vol. 176 no. 2
(2007),
pp. 969-981, ISSN 0016-6731 [doi] [abs]
- Chan, B; Durrett, R, A new coexistence result for competing contact processes,
Annals of Applied Probability, vol. 16 no. 3
(August, 2006),
pp. 1155-1165, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2260060 (2008h:60400)], [doi] [abs]
- Durrett, R, Random graph dynamics, Cambridge Series in Statistical and Probabilistic Mathematics,
Random Graph Dynamics
(January, 2006),
pp. 1-212, Cambridge University Press, Cambridge, ISBN 978-0-521-86656-9; 0-521-86656-1 [MR2271734 (2008c:05167)], [doi] [abs]
- Berestycki, N; Durrett, R, A phase transition in the random transposition random walk,
Probability Theory and Related Fields, vol. 136 no. 2
(January, 2006),
pp. 203-233, Springer Nature, ISSN 0178-8051 [MR2240787 (2007i:60009)], [doi] [abs]
- Durrett, R; Schweinsberg, J, Power laws for family sizes in a duplication model,
Annals of Probability, vol. 33 no. 6
(November, 2005),
pp. 2094-2126, Institute of Mathematical Statistics, ISSN 0091-1798 [MR2006j:60092], [doi] [abs]
- Durrett, R; Schweinsberg, J, A coalescent model for the effect of advantageous mutations on the genealogy of a population,
Stochastic Processes and their Applications, vol. 115 no. 10
(October, 2005),
pp. 1628-1657, Elsevier BV, ISSN 0304-4149 [MR2165337 (2006h:92026)], [doi] [abs]
- Blasiak, J; Durrett, R, Random Oxford graphs,
Stochastic Processes and their Applications, vol. 115 no. 8
(August, 2005),
pp. 1257-1278, Elsevier BV, ISSN 0304-4149 [MR2152374 (2006j:60008)], [doi] [abs]
- Schweinsberg, J; Durrett, R, Random partitions approximating the coalescence of lineages during a selective sweep,
Annals of Applied Probability, vol. 15 no. 3
(August, 2005),
pp. 1591-1651, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2152239 (2006c:92012)], [doi] [abs]
- Durrett, R; Levin, SA, Can stable social groups be maintained by homophilous imitation alone?,
Journal of Economic Behavior and Organization, vol. 57 no. 3
(July, 2005),
pp. 267-286, Elsevier BV [doi] [abs]
- York, TL; Durrett, RT; Tanksley, S; Nielsen, R, Bayesian and maximum likelihood estimation of genetic maps.,
Genetical research, vol. 85 no. 2
(April, 2005),
pp. 159-168 [doi] [abs]
- Zähle, I; Cox, JT; Durrett, R, The stepping stone model. II: Genealogies and the infinite sites model,
Annals of Applied Probability, vol. 15 no. 1 B
(February, 2005),
pp. 671-699, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2114986 (2006d:60157)], [doi] [abs]
- Durrett, R; Mytnik, L; Perkins, E, Competing super-brownian motions as limits of interacting particle systems,
Electronic Journal of Probability, vol. 10
(January, 2005),
pp. 1147-1220, Institute of Mathematical Statistics, ISSN 1083-6489 [MR2164042 (2006f:60052)], [doi] [abs]
- R. Durrett, Genome rearrangement,
in Statistical methods in molecular evolution, Stat. Biol. Health
(2005),
pp. 307--323, Springer, New York [MR2161835 (2006f:92021)]
- Schmidt, D; Durrett, R, Adaptive evolution drives the diversification of zinc-finger binding domains.,
Molecular biology and evolution, vol. 21 no. 12
(December, 2004),
pp. 2326-2339 [doi] [abs]
- Durrett, R; Schweinsberg, J, Approximating selective sweeps.,
Theoretical population biology, vol. 66 no. 2
(September, 2004),
pp. 129-138 [doi] [abs]
- Ward, R; Durrett, R, Subfunctionalization: How often does it occur? How long does it take?,
Theoretical population biology, vol. 66 no. 2
(September, 2004),
pp. 93-100 [doi] [abs]
- Sainudiin, R; Durrett, RT; Aquadro, CF; Nielsen, R, Microsatellite mutation models: insights from a comparison of humans and chimpanzees.,
Genetics, vol. 168 no. 1
(September, 2004),
pp. 383-395 [doi] [abs]
- Durrett, R; Nielsen, R; York, TL, Bayesian estimation of genomic distance.,
Genetics, vol. 166 no. 1
(January, 2004),
pp. 621-629 [doi] [abs]
- Durrett, R; Limic, V, Rigorous results for the NK model,
Annals of Probability, vol. 31 no. 4
(October, 2003),
pp. 1713-1753, Institute of Mathematical Statistics, ISSN 0091-1798 [doi] [abs]
- Durrett, R, Shuffling Chromosomes,
Journal of Theoretical Probability, vol. 16 no. 3
(July, 2003),
pp. 725-750, ISSN 0894-9840 [doi] [abs]
- Calabrese, P; Durrett, R, Dinucleotide repeats in the Drosophila and human genomes have complex, length-dependent mutation processes.,
Molecular biology and evolution, vol. 20 no. 5
(May, 2003),
pp. 715-725 [doi] [abs]
- Cox, T; Durrett, R, Erratum: The stepping stone model: New formulas expose old myths (The Annals of Applied Probability (2002) 12 (1348-1377)),
Annals of Applied Probability, vol. 13 no. 2
(May, 2003),
pp. 816, ISSN 1050-5164
- Durrett, R; Limic, V, A surprising poisson process arising from a species competition model,
Stochastic Processes and their Applications, vol. 102 no. 2
(December, 2002),
pp. 301-309, Elsevier BV, ISSN 0304-4149 [doi] [abs]
- Cox, JT; Durrett, R, The stepping stone model: New formulas expose old myths,
Annals of Applied Probability, vol. 12 no. 4
(November, 2002),
pp. 1348-1377, Institute of Mathematical Statistics [doi] [abs]
- Buttel, LA; Durrett, R; Levin, SA, Competition and species packing in patchy environments.,
Theoretical population biology, vol. 61 no. 3
(May, 2002),
pp. 265-276 [doi] [abs]
- Durrett, R; Kesten, H; Limic, V, Once edge-reinforced random walk on a tree,
Probability Theory and Related Fields, vol. 122 no. 4
(April, 2002),
pp. 567-592, Springer Nature [doi] [abs]
- Durrett, RT; Chen, K-Y; Tanksley, SD, A simple formula useful for positional cloning.,
Genetics, vol. 160 no. 1
(January, 2002),
pp. 353-355, ISSN 0016-6731 [doi] [abs]
- Durrett, R, Mutual invadability implies coexistence in spatial models,
Memoirs of the American Mathematical Society no. 740
(January, 2002) [doi] [abs]
- York, TL; Durrett, R; Nielsen, R, Bayesian estimation of the number of inversions in the history of two chromosomes.,
Journal of computational biology : a journal of computational molecular cell biology, vol. 9 no. 6
(January, 2002),
pp. 805-818 [doi] [abs]
- Balding, DJ; Carothers, AD; Marchini, JL; Cardon, LR; Vetta, A; Griffiths, B; Weir, BS; Hill, WG; Goldstein, D; Strimmer, K; Myers, S; Beaumont, MA; Glasbey, CA; Mayer, CD; Richardson, S; Marshall, C; Durrett, R; Nielsen, R; Visscher, PM; Knott, SA; Haley, CS; Ball, RD; Hackett, CA; Holmes, S; Husmeier, D; Jansen, RC; Ter Braak, CJF; Maliepaard, CA; Boer, MP; Joyce, P; Li, N; Stephens, M; Marcoulides, GA; Drezner, Z; Mardia, K; McVean, G; Meng, XL; Ochs, MF; Pagel, M; Sha, N; Vannucci, M; Sillanpää, MJ; Sisson, S; Yandell, BS; Jin, C; Satagopan, JM; Gaffney, PJ; Zeng, ZB; Broman, KW; Speed, TP; Fearnhead, P; Donnelly, P; Larget, B; Simon, DL; Kadane, JB; Nicholson, G; Smith, AV; Jónsson, F; Gústafsson, O; Stefánsson, K; Parmigiani, G; Garrett, ES; Anbazhagan, R; Gabrielson, E, Discussion on the meeting on 'statistical modelling and analysis of genetic data',
Journal of the Royal Statistical Society. Series B: Statistical Methodology, vol. 64 no. 4
(January, 2002),
pp. 737-775, WILEY, ISSN 1369-7412 [doi]
- Durrett, R, Mutual invadability implies coexistence in spatial models,
Memoirs of the American Mathematical Society no. 740
(January, 2002) [doi] [abs]
- Diaconis, P; Durrett, R, Chutes and Ladders in Markov Chains,
Journal of Theoretical Probability, vol. 14 no. 3
(December, 2001),
pp. 899-926 [doi] [abs]
- Calabrese, PP; Durrett, RT; Aquadro, CF, Dynamics of microsatellite divergence under stepwise mutation and proportional slippage/point mutation models.,
Genetics, vol. 159 no. 2
(October, 2001),
pp. 839-852, ISSN 0016-6731 [doi] [abs]
- Sundell, NM; Durrett, RT, Exponential distance statistics to detect the effects of population subdivision.,
Theoretical population biology, vol. 60 no. 2
(September, 2001),
pp. 107-116, ISSN 0040-5809 [doi] [abs]
- Durrett, R; Limic, V, On the quantity and quality of single nucleotide polymorphisms in the human genome,
Stochastic Processes and their Applications, vol. 93 no. 1
(May, 2001),
pp. 1-24, Elsevier BV [doi] [abs]
- Arkendra, DE; Ferguson, M; Sindi, S; Durrett, R, The equilibrium distribution for a generalized Sankoff-Ferretti model accurately predicts chromosome size distributions in a wide variety of species,
Journal of Applied Probability, vol. 38 no. 2
(January, 2001),
pp. 324-334, Cambridge University Press (CUP), ISSN 0021-9002 [doi] [abs]
- Broughton, RE; Stanley, SE; Durrett, RT, Quantification of homoplasy for nucleotide transitions and transversions and a reexamination of assumptions in weighted phylogenetic analysis.,
Systematic biology, vol. 49 no. 4
(December, 2000),
pp. 617-627 [doi] [abs]
- Kruglyak, S; Durrett, R; Schug, MD; Aquadro, CF, Distribution and abundance of microsatellites in the yeast genome can Be explained by a balance between slippage events and point mutations.,
Molecular biology and evolution, vol. 17 no. 8
(August, 2000),
pp. 1210-1219, ISSN 0737-4038 [doi] [abs]
- Durrett, R; Levin, S, Lessons on pattern formation from planet WATOR.,
Journal of theoretical biology, vol. 205 no. 2
(July, 2000),
pp. 201-214, ISSN 0022-5193 [doi] [abs]
- Vision, TJ; Brown, DG; Shmoys, DB; Durrett, RT; Tanksley, SD, Selective mapping: a strategy for optimizing the construction of high-density linkage maps.,
Genetics, vol. 155 no. 1
(May, 2000),
pp. 407-420 [doi] [abs]
- Liu, YC; Durrett, R; Milgroom, MG, A spatially-structured stochastic model to simulate heterogenous transmission of viruses in fungal populations,
Ecological Modelling, vol. 127 no. 2-3
(March, 2000),
pp. 291-308, Elsevier BV [doi] [abs]
- Durrett, R; Buttel, L; Harrison, R, Spatial models for hybrid zones.,
Heredity, vol. 84 ( Pt 1) no. 1
(January, 2000),
pp. 9-19, ISSN 0018-067X [doi] [abs]
- Cox, JT; Durrett, R; Perkins, EA, Rescaled voter models converge to super-Brownian motion,
Annals of Probability, vol. 28 no. 1
(January, 2000),
pp. 185-234, Institute of Mathematical Statistics [doi] [abs]
- Durrett, R; Schinazi, RB, Boundary Modified Contact Processes,
Journal of Theoretical Probability, vol. 13 no. 2
(January, 2000),
pp. 575-594 [doi] [abs]
- Molofsky, J; Durrett, R; Dushoff, J; Griffeath, D; Levin, S, Local frequency dependence and global coexistence.,
Theoretical population biology, vol. 55 no. 3
(June, 1999),
pp. 270-282, ISSN 0040-5809 [doi] [abs]
- Durrett, R, Stochastic spatial models,
SIAM Review, vol. 41 no. 4
(January, 1999),
pp. 677-718, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
- Durrett, R; Perkins, EA, Rescaled contact processes converge to super-Brownian motion in two or more dimensions,
Probability Theory and Related Fields, vol. 114 no. 3
(January, 1999),
pp. 309-399, Springer Nature [doi] [abs]
- Durrett, R; Granovsky, BL; Gueron, S, The Equilibrium Behavior of Reversible Coagulation-Fragmentation Processes,
Journal of Theoretical Probability, vol. 12 no. 2
(January, 1999),
pp. 447-474 [doi] [abs]
- Durrett, R; Kruglyak, S, A new stochastic model of microsatellite evolution,
Journal of Applied Probability, vol. 36 no. 3
(January, 1999),
pp. 621-631, Cambridge University Press (CUP) [doi] [abs]
- Kruglyak, S; Durrett, RT; Schug, MD; Aquadro, CF, Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 95 no. 18
(September, 1998),
pp. 10774-10778, ISSN 0027-8424 [doi] [abs]
- Durrett, R; Levin, S, Spatial aspects of interspecific competition.,
Theoretical population biology, vol. 53 no. 1
(February, 1998),
pp. 30-43, ISSN 0040-5809 [doi] [abs]
- Durrett, R; Levin, S, Erratum: Spatial aspects of interspecific competition (Theoretical Population Biology (1998) 53:1 (30-43)),
Theoretical Population Biology, vol. 53 no. 3
(January, 1998),
pp. 284, Elsevier BV [doi]
- Bramson, M; Cox, JT; Durrett, R, A spatial model for the abundance of species,
Annals of Probability, vol. 26 no. 2
(January, 1998),
pp. 658-709, Institute of Mathematical Statistics [doi] [abs]
- Durrett, R; Levin, S, Allelopathy in spatially distributed populations,
Journal of Theoretical Biology, vol. 185 no. 2
(March, 1997),
pp. 165-171, Elsevier BV [doi] [abs]
- Allouba, H; Durrett, R; Hawkes, J; Perkins, E, Super-Tree Random Measures,
Journal of Theoretical Probability, vol. 10 no. 3
(January, 1997),
pp. 773-794 [doi] [abs]
- Durrett, R; Neuhauser, C, Coexistence results for some competition models,
Annals of Applied Probability, vol. 7 no. 1
(January, 1997),
pp. 10-45, Institute of Mathematical Statistics [doi] [abs]
- Chen, ZQ; Durrett, R; Ma, G, Holomorphic diffusions and boundary behavior of harmonic functions,
Annals of Probability, vol. 25 no. 3
(January, 1997),
pp. 1103-1134, Institute of Mathematical Statistics [doi] [abs]
- Durrett, R; Levin, S, Spatial models for species-area curves,
Journal of Theoretical Biology, vol. 179 no. 2
(March, 1996),
pp. 119-127, Elsevier BV [doi] [abs]
- Bramson, M; Cox, JT; Durrett, R, Spatial models for species area curves,
Annals of Probability, vol. 24 no. 4
(January, 1996),
pp. 1727-1751, Institute of Mathematical Statistics [doi] [abs]
- Cox, JT; Durrett, R, Hybrid zones and voter model interfaces,
Bernoulli, vol. 1 no. 4
(January, 1995),
pp. 343-370, Bernoulli Society for Mathematical Statistics and Probability [doi] [abs]
- Durrett, R; Swindle, G, Coexistence results for catalysts,
Probability Theory and Related Fields, vol. 98 no. 4
(December, 1994),
pp. 489-515, Springer Nature, ISSN 0178-8051 [doi] [abs]
- Durrett, R; Levin, S, The importance of being discrete (and spatial),
Theoretical Population Biology, vol. 46 no. 3
(January, 1994),
pp. 363-394, Elsevier BV [doi] [abs]
- Durrett, R; Levin, SA, Stochastic spatial models: A user's guide to ecological applications,
Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 343 no. 1305
(January, 1994),
pp. 329-350, The Royal Society, ISSN 0962-8436 [doi]
- Durrett, R; Griffeath, D, Asymptotic behavior of excitable cellular automata,
Experimental Mathematics, vol. 2 no. 3
(January, 1993),
pp. 183-208, Informa UK Limited [doi] [abs]
- Durrett, RT; Rogers, LCG, Asymptotic behavior of Brownian polymers,
Probability Theory and Related Fields, vol. 92 no. 3
(September, 1992),
pp. 337-349, Springer Nature, ISSN 0178-8051 [doi] [abs]
- Durrett, R, Multicolor particle systems with large threshold and range,
Journal of Theoretical Probability, vol. 5 no. 1
(January, 1992),
pp. 127-152, Springer Nature, ISSN 0894-9840 [doi] [abs]
- Durrett, R; Steif, JE, Some rigorous results for the Greenberg-Hastings Model,
Journal of Theoretical Probability, vol. 4 no. 4
(October, 1991),
pp. 669-690, Springer Nature, ISSN 0894-9840 [doi] [abs]
- Cox, JT; Durrett, R; Schinazi, R, The critical contact process seen from the right edge,
Probability Theory and Related Fields, vol. 87 no. 3
(September, 1991),
pp. 325-332, Springer Nature, ISSN 0178-8051 [doi] [abs]
- Durrett, R; Møller, AM, Complete convergence theorem for a competition model,
Probability Theory and Related Fields, vol. 88 no. 1
(March, 1991),
pp. 121-136, Springer Nature, ISSN 0178-8051 [doi] [abs]
- Durrett, R; Swindle, G, Are there bushes in a forest?,
Stochastic Processes and their Applications, vol. 37 no. 1
(January, 1991),
pp. 19-31, Elsevier BV, ISSN 0304-4149 [doi] [abs]
- Durrett, R; Kesten, H; Waymire, E, On weighted heights of random trees,
Journal of Theoretical Probability, vol. 4 no. 1
(January, 1991),
pp. 223-237, Springer Nature, ISSN 0894-9840 [doi] [abs]
- Bramson, M; Wan-ding, D; Durrett, R, Annihilating branching processes,
Stochastic Processes and their Applications, vol. 37 no. 1
(January, 1991),
pp. 1-17, Elsevier BV, ISSN 0304-4149 [doi] [abs]
- Jinwen, C; Durrett, R; Xiufang, L, Exponential convergence for one dimensional contact processes,
Acta Mathematica Sinica, vol. 6 no. 4
(December, 1990),
pp. 349-353, Springer Nature, ISSN 1439-8516 [doi] [abs]
- Ding, WD; Durrett, R; Liggett, TM, Ergodicity of reversible reaction diffusion processes,
Probability Theory and Related Fields, vol. 85 no. 1
(March, 1990),
pp. 13-26, Springer Nature, ISSN 0178-8051 [doi] [abs]
- Cox, JT; Durrett, R, Large deviations for independent random walks,
Probability Theory and Related Fields, vol. 84 no. 1
(March, 1990),
pp. 67-82, Springer Nature, ISSN 0178-8051 [doi] [abs]
- Durrett, R; Tanaka, NI, Scaling inequalities for oriented percolation,
Journal of Statistical Physics, vol. 55 no. 5-6
(June, 1989),
pp. 981-995, Springer Nature, ISSN 0022-4715 [doi] [abs]
- Durrett, R; Schonmann, RH; Tanaka, NI, Correlation lengths for oriented percolation,
Journal of Statistical Physics, vol. 55 no. 5-6
(June, 1989),
pp. 965-979, Springer Nature, ISSN 0022-4715 [doi] [abs]
- Bramson, M; Durrett, R, A simple proof of the stability criterion of Gray and Griffeath,
Probability Theory and Related Fields, vol. 80 no. 2
(December, 1988),
pp. 293-298, Springer Nature America, Inc, ISSN 0178-8051 [doi] [abs]
- Durrett, R; Schonmann, RH, Large deviations for the contact process and two dimensional percolation,
Probability Theory and Related Fields, vol. 77 no. 4
(December, 1988),
pp. 583-603, Springer Nature, ISSN 0178-8051 [doi] [abs]
- Durrett, R, Crabgrass, measles, and gypsy moths: An introduction to interacting particle systems,
The Mathematical Intelligencer, vol. 10 no. 2
(June, 1988),
pp. 37-47, Springer Nature, ISSN 0343-6993 [doi]
- Bramson, M; Durrett, R, Random walk in random environment: A counterexample?,
Communications in Mathematical Physics, vol. 119 no. 2
(June, 1988),
pp. 199-211, Springer Nature, ISSN 0010-3616 [doi] [abs]
- Chayes, JT; Chayes, L; Durrett, R, Connectivity properties of Mandelbrot's percolation process,
Probability Theory and Related Fields, vol. 77 no. 3
(March, 1988),
pp. 307-324, Springer Nature America, Inc, ISSN 0178-8051 [doi] [abs]
- Cox, JT; Durrett, R, Limit theorems for the spread of epidemics and forest fires,
Stochastic Processes and their Applications, vol. 30 no. 2
(January, 1988),
pp. 171-191, Elsevier BV, ISSN 0304-4149 [doi] [abs]
- Durrett, R, Crabgrass, measles, and gypsy moths: An introduction to modern probability,
Bulletin of the American Mathematical Society, vol. 18 no. 2
(January, 1988),
pp. 117-143, American Mathematical Society (AMS) [doi]
- Chayes, JT; Chayes, L; Durrett, R, Inhomogeneous percolation problems and incipient infinite clusters,
Journal of Physics A: Mathematical and General, vol. 20 no. 6
(December, 1987),
pp. 1521-1530, IOP Publishing, ISSN 0305-4470 [doi] [abs]
- Brennan, MD; Durrett, R, Splitting intervals II: Limit laws for lengths,
Probability Theory and Related Fields, vol. 75 no. 1
(May, 1987),
pp. 109-127, Springer Nature America, Inc, ISSN 0178-8051 [doi] [abs]
- Chayes, JT; Chayes, L; Durrett, R, Critical behavior of the two-dimensional first passage time,
Journal of Statistical Physics, vol. 45 no. 5-6
(December, 1986),
pp. 933-951, Springer Nature, ISSN 0022-4715 [doi] [abs]
- Durrett, R, Multidimensional random walks in random environments with subclassical limiting behavior,
Communications in Mathematical Physics, vol. 104 no. 1
(March, 1986),
pp. 87-102, Springer Nature, ISSN 0010-3616 [doi] [abs]
- Durrett, R, Some general results concerning the critical exponents of percolation processes,
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 69 no. 3
(September, 1985),
pp. 421-437, Springer Nature America, Inc, ISSN 0044-3719 [doi] [abs]
- Durrett, R; Nguyen, B, Thermodynamic inequalities for percolation,
Communications in Mathematical Physics, vol. 99 no. 2
(June, 1985),
pp. 253-269, Springer Nature, ISSN 0010-3616 [doi] [abs]
- Durrett, R; Liggett, TM, Fixed points of the smoothing transformation,
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 64 no. 3
(September, 1983),
pp. 275-301, Springer Nature, ISSN 0044-3719 [doi] [abs]
- Durrett, R, Maxima of branching random walks,
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 62 no. 2
(June, 1983),
pp. 165-170, Springer Nature America, Inc, ISSN 0044-3719 [doi] [abs]
- Chung, KL; Durrett, R; Zhao, Z, Extension of domains with finite gauge,
Mathematische Annalen, vol. 264 no. 1
(March, 1983),
pp. 73-79, Springer Nature, ISSN 0025-5831 [doi]
- Cox, JT; Durrett, R, Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas,
Mathematical Proceedings of the Cambridge Philosophical Society, vol. 93 no. 1
(January, 1983),
pp. 151-162, Cambridge University Press (CUP) [doi] [abs]
- Durrett, R; Griffeath, D, Contact processes in several dimensions,
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 59 no. 4
(December, 1982),
pp. 535-552, Springer Nature America, Inc, ISSN 0044-3719 [doi]
- Durrett, R, An introduction to infinite particle systems,
Stochastic Processes and their Applications, vol. 11 no. 2
(January, 1981),
pp. 109-150, Elsevier BV, ISSN 0304-4149 [doi] [abs]
- Durrett, R, Conditioned limit theorems for random walks with negative drift,
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 52 no. 3
(January, 1980),
pp. 277-287, Springer Nature, ISSN 0044-3719 [doi] [abs]
- Durrett, R, Maxima of branching random walks vs. independent random walks,
Stochastic Processes and their Applications, vol. 9 no. 2
(January, 1979),
pp. 117-135, Elsevier BV, ISSN 0304-4149 [doi] [abs]
- Anthony, PF; Durrett, R; Pulec, JL; Hartstone, JL, A new parameter in brain stem evoked response: Component wave areas,
Laryngoscope, vol. 89 no. 10 I
(1979),
pp. 1569-1578 [doi] [abs]
- Durrett, R, The genealogy of critical branching processes,
Stochastic Processes and their Applications, vol. 8 no. 1
(January, 1978),
pp. 101-116, Elsevier BV, ISSN 0304-4149 [doi] [abs]
- Durrett, RT; Resnick, SI, Weak convergence with random indices,
Stochastic Processes and their Applications, vol. 5 no. 3
(January, 1977),
pp. 213-220, Elsevier BV, ISSN 0304-4149 [doi] [abs]
- Chung, KL; Durrett, R, Downcrossings and local time,
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 35 no. 2
(June, 1976),
pp. 147-149, Springer Nature America, Inc, ISSN 0044-3719 [doi]
- Durrett, RT; Ghurye, SG, WAITING TIMES WITHOUT MEMORY.,
J Appl Probab, vol. 13 no. 1
(January, 1976),
pp. 65-75 [doi] [abs]
Papers Accepted
- R. Durrett and S. Moseley, Spatial Moran Models. I. Tunneling in the Neutral Case,
Annals Applied Probability
(2013)
Papers Submitted
- S. Magura, V. Pong, D. Sivakoff, and R. Durrett, Two evolving social network models
(2013)
- R. Durrett, Phase transition in a meta-population version of Schelling's model
(2012)
- R. Durrett, J. Foo, and K. Leder, Spatial Moran Models II. Tumor growth and progression
(2012)
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dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
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