Publications of Gregory F Lawler
Books
- Gregory F. Lawler and Lester N. Coyle, Lectures on Contemporary Probability,
AMS Student Mathematical Library (1999)
- Gregory F. Lawler, Introduction to Stochastic Processes,
CRC Chapman and Hall (1995)
- Gregory F. Lawler, Intersections of Random Walks,
Birkhauser-Boston (1991, softcover edition 1996)
Papers Published
- Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents I: half-plane exponents,
Acta. Math. 187 (2001), 237--273
- Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents II: plane exponents,
Acta Math. 187 (2001), 275--308
- Gregory F. Lawler, Oded Schramm, and Wendelin Werner, One-arm exponent for critical 2D percolation,
Electronic J. of Probability, 7 (2002), paper no. 2
- Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Values of Brownian intersection exponents III: Two-sided exponents,
Ann. Inst. Henri Poincare' 38 (2002), pp 109--123
- Gregory F. Lawler, Oded Schramm, and Wendelin Werner, The dimension of the planar Brownian frontier is 4/3,
Math. Research Letters 8 (2001), 401--411
- Gregory F. Lawler and Wendelin Werner, Universality for conformally invariant intersection exponents,
J. European Math. Soc. 2 (2000) , 291--328
- Gregory F. Lawler, Strict concavity of the half plane intersection exponent for planar Brownian motion,
Electronic Journal of Probability 5 (2000), paper no. 8
- Gregory F. Lawler, Emily Puckette, The intersection exponent for simple random walk,
Combinatorics, Probability, and Computing 9 (2000), 441--464
- Gregory F. Lawler and Wendelin Werner, Intersection exponents for planar Brownian motion,
Annals of Probability 27 (1999), 1601-1642
- Gregory F. Lawler, A lower bound on the growth exponent for loop-erased walk in two dimensions,
ESAIM: Probability and Statistics 3 (1999),1-21
- Gregory F. Lawler, Multifractal nature of two dimensional simple random walk paths,
Random Walks and Discrete Potential Theory, M. Picardello and W. Woess, ed., Cambridge University Press (1999), 231--264.
- Gregory F. Lawler, Loop-erased random walk,
Perplexing Problems in Probability, Birkhauser-Boston (1999), 197--217
- Gregory F. Lawler, Geometric and fractal properties of Brownian motion and random walk paths in two and three dimensions,
Bolyai Mathematical Society Studies, 9 (1999), 219-258
- Gregory F. Lawler, Strict concavity of the intersection exponent for Brownian motion in two and three dimensions,
Mathematical Physics Electronic Journal 5 (1998), #5
- Gregory F. Lawler, Loop-erased walks intersect infinitely often in four dimensions,
Electronic Communications in Probability 3 (1998), 35-42
- Gregory F. Lawler, Emily E. Puckette, The disconnection exponent for simple random walk,
Israel Journal of Mathematics 99 (1997), 109-122.
- Gregory F. Lawler, Hausdorff dimension of cut points for Brownian motion,
Electronic Journal of Probability 1 (1996), #2
- Gregory F. Lawler, Cut points for simple random walk,
Electronic Journal of Probability 1 (1996), #13
- Gregory F. Lawler, The dimension of the frontier of planar Brownian motion,
Electronic Communications in Probability 1 (1996), 29-47
- Gregory F. Lawler, Subdiffusive fluctuations for internal diffusion limited aggregation,
Annals of Probability 23 (1995), 71-86
- Gregory F. Lawler, The logarithmic correction for loop-erased walk in four dimensions,
Proceedings of the Conference in Honor of J.P. Kahane, special issue of Journal of Fourier Analysis and Applications, CRC Press (1995), 347-362
- Gregory F. Lawler, Recurrence and transience for a card shuffling model,
Combinatorics, Probability, and Computing 4 (1995), 133-142
- Gregory F. Lawler, Nonintersecting planar Brownian motions,
Mathematical Physics Electronic Journal 1 (1995), #4
- Gregory F. Lawler, Random walks: simple and self-avoiding,
Topics in Comtemporary Probability and its Applications, J. Laurie Snell, ed.,
CRC (1995), 55-74
- Gregory F. Lawler, Random walks, harmonic measure, and Laplacian growth models,
Probability and Phase Transitions, ed. G. Grimmett, Kluwer (1994), 191-208
- Gregory F. Lawler and Thomas Polaski, Harnack inequalities
and difference estimates for random walks with infinite range,
Journal of Theoretical Probability, 6 (1993), 781-802
- Gregory F. Lawler, On the covering time of a disc by simple random walk in two
dimensions,
Seminar on Stochastic Processes, 1992, Birkh\"auser-Boston
(1993), 189-208
- Bertrand Duplantier, Gregory F. Lawler, Jean-Francois Le Gall, and Terry Lyons, The geometry ofthe Brownian curve,
Bull. Sci. Math, 2eme serie, 117 (1993), 91-106
- Gregory F. Lawler, A discrete analogue of a theorem of Makarov,
Combinatorics, Probability, and Computing 2 (1993), 181-200
- Harry Kesten and Gregory F. Lawler, A necessary condition for making money from fair
games,
Annals of Probability 20 (1992), 855--882
- Gregory F. Lawler, Maury Bramson, and David Griffeath, Internal diffusion
limited aggregation,
Annals of Probability 20 (1992), 2117-2140
- Gregory F. Lawler, Escape probabilities for slowly recurrent sets,
Probability Theory and Related Fields 94 (1992), 91-117
- Gregory F. Lawler, $L$-shapes for the logarithmic $\eta$-model for DLA in three dimensions,
Seminar on Stochastic Processes, 1991, Birkh\"auser-Boston (1992), 97--122
- Gregory F. Lawler, Estimates for differences and Harnack's inequality for difference
operators coming
from random walks with symmetric, spatially inhomogeneous increments,
Proceedings of London Mathematical Society 63 (1991), 552--568
- Gregory F. Lawler, Intersection probabilities for random walks,
Mathematics of Random Media, AMS Lectures in Applied Mathematics 27 (1991), 73--86
- Richard Durrett, Harry Kesten, and Gregory F. Lawler, Making money from fair games,
Random Walks, Brownian Motion and Interacting Particle Systems, Birkh\"auser, Boston (1991), 255-267
- Gregory F. Lawler, Problems on the geometry of random walk paths,
Probability Models in Mathematical Physics, World Scientific (1991), 135--143
- Krzysztof Burdzy and Gregory F. Lawler, Non-intersection exponents for random walk and
Brownian motion.
Part I: Existence and an invariance principle,
Probability Theory and
Related Fields 84 (1990), 393--410
- Krzysztof Burdzy and Gregory F. Lawler, Non-intersection exponents for random walk and
Brownian motion.
Part II: Estimates
and applications to a random fractal,
Annals of Probability 18 (1990), 981--1009
- Gregory F. Lawler, The Edwards model and the weakly self-avoiding walk,
Journal of
Physics A 23 (1990), 1467--1470#
- Krzysztof Burdzy and Gregory F. Lawler, Rigorous exponent inequalities for random
walks,
Journal of Physics A 23 (1990), L23--L28
- J. Roerdink, K. Shuler, and Gregory F. Lawler, Diffusion in lattices with
anisotropic scatterers,
Journal of Statistical Physics 59 (1990) ,
23--52
- Gregory F. Lawler, Low density estimates for a two-state random walk in random environment,
Journal of Mathematical Physics 30 (1989), 145-157
- Gregory F. Lawler and John Sylvester, Determining resistances from boundary measurements
in finite networks,
SIAM Journal on Discrete Mathematics 2 (1989),
231-239
- Gregory F. Lawler, The infinite self-avoiding walk in high dimensions,
Annals of Probability
17 (1989), 1367--1376
- Gregory F. Lawler, Intersections of random walks with random sets,
Israel Journal of
Mathematics 65 (1989), 113-132
- Krzysztof Burdzy, Gregory F. Lawler, and Thomas Polaski, On the critical exponent for random walk intersections,
Journal of Statistical Physics { 56 (1989), 1-12
- Joe Blum, Gregory F. Lawler, Michael Reed, and Insun Shin, The effect of cytoskeletal
geometry on intracellular diffusion,
Biophysical Journal 56 (1989),
995--1005
- Gregory F. Lawler, Loop-erased self-avoiding random walk in two and three dimensions,
Journal of Statistical Physics 50 (1988), 91-108
- Gregory F. Lawler and Alan Sokal, Bounds on the L_2 spectrum for Markov chains and Markov
processes: a generalization of Cheeger's inequality,
Trans. Amer. Math.
Soc. 309 (1988), 557-580.
- Gregory F. Lawler, Loop-erased self-avoiding random walk and the Laplacian random walk,
Journal of Physics A. 20 (1987), 4565-4568
- Gregory F. Lawler, Expected hitting time for a random walk on a connected graph,
Discrete Mathematics 61 (1986), 85-92
- Gregory F. Lawler, Gaussian behavior of loop-erased self-avoiding random walk in four dimensions,
Duke Mathematical Journal 53 (1986), 249-270
- Gregory F. Lawler, Intersections of random walks in four dimensions II,
Comm. Math.
Phys. 97 (1985), 583-594
- Gregory F. Lawler, Intersections of simple random walks,
AMS Contemporary Mathematics 41 (1985), 281-289
- Gregory F. Lawler and Robert Vanderbei, Markov strategies for optimal control problems indexed by a partially ordered set,
Annals of Prob. 11 (1983), 642-647
- Gregory F. Lawler, A discrete stochastic integral inequality and balanced random walk in a random environment,
Duke Mathematical Journal 50 (1983), 1261-1274
- Gregory F. Lawler, A connective constant for loop-erased self-avoiding random walk,
J. Appl. Prob. 20
(1983), 264-276
- Gregory F. Lawler, The probability of intersection of independent random walks in four dimensions,
Commun. Math.Phys 86 (1982), 539-554
- Gregory F. Lawler, Weak convergence of a random walk in a random environment,
Commun.
Math. Phys. 87 (1982), 81-87
- Gregory F. Lawler, A self-avoiding random walk,
Duke Mathematical Journal 47 (1980), 655-694.
Papers Accepted
- Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Sharp estimates for Brownian non-intersection probabilities,
to appear in In and Out of Equilbrium, Birkhauser
, accepted 2001
- Gregory F. Lawler, Oded Schramm, and Wendelin Werner, Analyticity of intersection exponents for planar Brownian motion,
Acta Math.
, accepted 2001
- Gregory F. Lawler, Cut times for Brownian motion and random walk,
Proceedings of Conference in Honor of Paul Erdos
, accepted 2000
Preprints
- Gregory F. Lawler, Oded Schramm, and Wendelin Werner, On the scaling limit of planar self-avoiding walk
, preprint 2002
- Gregory F. Lawler, Oded Scrhamm, and Wendelin Werner, Conformal invariance of planar loop-erased random walk and uniform spanning trees
, preprint 2002
- Gregory F. Lawler, An introduction to the stochastic Loewner evolution
, preprint 2001
- Gregory F. Lawler, A note on the Green's function for random walk in four dimensions,
Duke University Math Preprint 94-03
, preprint 1998
- Gregory F. Lawler, The frontier of a Brownian path is multifractal,
preprint
, preprint 1998
Book Reviews
- Gregory F. Lawler, Self-Avoiding Walk (N. Madras and G. Slade),
Annals of Probability 27 (1999), 606-609
- Gregory F. Lawler, Aspects and Applications of Random Walk (G. Weiss),
SIAM Review \bf 37 (1995) 470-471
- Gregory F. Lawler, Random Walks, Brownian Motion, and Interacting Particle Systems, a Festschrift for Frank Spitzer (R. Durrett, H. Kesten, ed.),
Metrika 41 (1994) 254-255