Math @ Duke

Papers Published
 Hairer, M; Mattingly, J, The strong Feller property for singular stochastic PDEs
(2016) [abs]
 Tempkin, JOB; Koten, BV; Mattingly, JC; Dinner, AR; Weare, J, Trajectory stratification of stochastic dynamics
(2016) [abs]
 Herzog, DP; Mattingly, JC, A practical criterion for positivity of transition densities,
Nonlinearity, vol. 28 no. 8
(August, 2015),
pp. 28232845, ISSN 09517715 [repository], [doi]
 Lawley, SD; Mattingly, JC; Reed, MC, Stochastic Switching in Infinite Dimensions with Applications to Random Parabolic PDE,
SIAM Journal on Mathematical Analysis, vol. 47 no. 4
(January, 2015),
pp. 30353063, ISSN 00361410 [repository], [doi]
 Munch, E; Turner, K; Bendich, P; Mukherjee, S; Mattingly, J; Harer, J, Probabilistic Fréchet means for time varying persistence diagrams,
Electronic Journal of Statistics, vol. 9 no. 1
(January, 2015),
pp. 11731204 [1307.6530v3], [doi] [abs]
 Huckemann, S; Mattingly, J; Miller, E; Nolen, J, Sticky central limit theorems at isolated hyperbolic planar singularities,
Electronic Journal of Probability, vol. 20
(2015) [repository], [doi]
 Herzog, D; Mattingly, J, Noiseinduced stabilization of planar flows II,
Electronic Journal of Probability, vol. 20
(2015) [repository], [doi] [abs]
 Luo, S; Mattingly, JC, Scaling limits of a model for selection at two scales
(2015) [1507.00397v1] [abs]
 Mattingly, JC; Pardoux, E, Invariant measure selection by noise. An example,
Discrete and Continuous Dynamical Systems, vol. 34 no. 10
(2014),
pp. 42234257, ISSN 10780947 [arXiv:1403.3593], [repository], [doi] [abs]
 Hotz, T; Huckemann, S; Le, H; Marron, JS; Mattingly, JC; Miller, E; Nolen, J; Owen, M; Patrangenaru, V; Skwerer, S, Sticky central limit theorems on open books,
The annals of applied probability : an official journal of the Institute of Mathematical Statistics, vol. 23 no. 6
(2013),
pp. 22382258, ISSN 10505164 [arXiv:1202.4267], [12AAP899], [doi] [abs]
 Luo, S; Reed, M; Mattingly, JC; Koelle, K, The impact of host immune status on the withinhost and population dynamics of antigenic immune escape.,
Journal of the Royal Society Interface, vol. 9 no. 75
(October, 2012),
pp. 26032613 [22572027], [doi] [abs]
 with Mattingly, JC; McKinley, SA; Pillai, NS, Geometric ergodicity of a beadspring pair with stochastic Stokes forcing,
Stochastic Processes and their Applications, vol. 122 no. 12
(2012),
pp. 39533979, ISSN 03044149 [MR2971721], [0902.4496], [repository], [doi] [abs]
 with Athreyaz, A; Kolba, T; Mattingly, JC, Propagating lyapunov functions to prove noiseinduced stabilization,
Electronic Journal of Probability, vol. 17
(November 2, 2012),
pp. 138, ISSN 10836489 [math/111.1755], [repository], [doi] [abs]
 Porporato, A; Kramer, PR; Cassiani, M; Daly, E; Mattingly, J, Local kinetic interpretation of entropy production through reversed diffusion.,
Physical Review E  Statistical, Nonlinear, and Soft Matter Physics, vol. 84 no. 4 Pt 1
(Fall, 2011),
pp. 041142 [22181122], [doi] [abs]
 Koelle, K; Ratmann, O; Rasmussen, DA; Pasour, V; Mattingly, J, A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses,
Proceedings of the Royal Society of London: Biological Sciences, vol. 278 no. 1725
(May 4, 2011),
pp. 37233730, ISSN 09628452 [repository], [doi] [abs]
 with Hairer, M; Mattingly, JC; Scheutzow, M, Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations,
Probability Theory and Related Fields, vol. 149 no. 1
(2011),
pp. 223259, ISSN 01788051 [MR2531551], [0902.4495], [repository], [doi] [abs]
 with Anderson, DF; Mattingly, JC, A weak trapezoidal method for a class of stochastic differential equations,
Communications in Mathematical Sciences, vol. 9 no. 1
(March, 2011),
pp. 301318, ISSN 15396746 [0906.3475], [repository] [abs]
 with Hairer, M; Mattingly, JC, A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs,
Electronic Journal of Probability, vol. 16 no. 23
(2011),
pp. 658738, ISSN 10836489 [arXiv:0808.1361], [repository] [abs]
 with Mattingly, JC; Stuart, AM; Tretyakov, MV, Convergence of numerical timeaveraging and stationary measures via Poisson equations,
SIAM Journal on Numerical Analysis, vol. 48 no. 2
(2010),
pp. 552577, ISSN 00361429 [MR2669996], [0908.4450], [repository], [doi] [abs]
 Hairer, M; Mattingly, JC, Slow energy dissipation in anharmonic oscillator chains,
Communications on Pure & Applied Mathematics, vol. 62 no. 8
(2008),
pp. 9991032, ISSN 00103640 [MR2531551], [arXiv:0712.3884], [doi] [abs]
 with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains
(August, 2008) [arXiv:0810.2777] [abs]
 Mattingly, JC; Suidan, TM, Transition measures for the stochastic Burgers equation,
in Integrable systems and random matrices, Contemp. Math.,
Contemporary Mathematics, vol. 458
(2008),
pp. 409418, Amer. Math. Soc., Providence, RI, ISSN 02714132, ISBN 9780821842409 [MR2411921], [Gateway.cgi]
 with Iyer, G; Mattingly, J, A stochasticLagrangian particle system for the NavierStokes equations,
Nonlinearity, vol. 21 no. 11
(2008),
pp. 25372553, ISSN 09517715 [MR2448230 (2009h:76060)], [arXiv:0803.1222], [doi] [abs]
 with Hairer, M; Mattingly, JC; Martin Hairer, , Spectral gaps in Wasserstein distances and the 2D stochastic NavierStokes equationsSpectral gaps in Wasserstein distances and the 2D stochastic NavierStokes equations,
Annals of Probability no. 6
(2008),
pp. 9931032 [MR2478676], [math.PR/0602479] [abs]
 Mattingly, JC; Anderson, DF, Propagation of fluctuations in biochemical systems, II: nonlinear chains,
IET systems biology, vol. 1 no. 6
(November, 2007),
pp. 313325, ISSN 17518849 [repository], [doi]
 Anderson, DF; Mattingly, JC; Nijhout, HF; Reed, MC, Propagation of fluctuations in biochemical systems, I: Linear SSC networks,
Bulletin of Mathematical Biology, vol. 69 no. 6
(August, 2007),
pp. 17911813, ISSN 00928240 [MR2329180], [17457656], [doi] [abs]
 Lamba, H; Mattingly, JC; Stuart, AM, An adaptive EulerMaruyama scheme for SDEs: Convergence and stability,
IMA Journal of Numerical Analysis, vol. 27 no. 3
(2007),
pp. 479506, ISSN 02724979 [MR2337577], [math.PR/0409057]], [doi] [abs] [author's comments]
 Mattingly, JC; Suidan, T; VandenEijnden, E, Simple systems with anomalous dissipation and energy cascade,
Communications in Mathematical Physics, vol. 276 no. 1
(2007),
pp. 189220, ISSN 00103616 [MR2342292 (2008m:37135)], [mathph/0607047], [doi] [abs]
 Bakhtin, Y; Mattingly, JC, Malliavin calculus for infinitedimensional systems with additive noise,
Journal of Functional Analysis, vol. 249 no. 2
(2007),
pp. 307353, ISSN 00221236 [MR2345335], [math.PR/0610754], [doi] [abs]
 Mattingly, JC; Suidan, TM; VandenEijnden, E, Anomalous dissipation in a stochastically forced infinitedimensional system of coupled oscillators,
Journal of Statistical Physics, vol. 128 no. 5
(2007),
pp. 11451152, ISSN 00224715 [MR2348788], [mathph/0607047], [doi] [abs]
 Nijhout, HF; Reed, MC; Anderson, DF; Mattingly, JC; James, SJ; Ulrich, CM, Longrange allosteric interactions between the folate and methionine cycles stabilize DNA methylation reaction rate.,
Epigenetics : official journal of the DNA Methylation Society, vol. 1 no. 2
(April/May 2006),
pp. 8187, ISSN 15592294 [17998813] [abs]
 Mattingly, JC; Pardoux, É, Malliavin calculus for the stochastic 2D NavierStokes equation,
Communications on Pure & Applied Mathematics, vol. 59 no. 12
(December, 2006),
pp. 17421790, ISSN 00103640 [math.PR/0407215], [doi] [abs]
 Hairer, M; Mattingly, JC, Ergodicity of the 2D NavierStokes equations with degenerate stochastic forcing,
Annals of Mathematics, vol. 164 no. 3
(November, 2006),
pp. 9931032, ISSN 0003486X [math.PR/0406087] [abs]
 Mattingly, JC; Suidan, TM, The small scales of the stochastic NavierStokes equations under rough forcing,
Journal of Statistical Physics, vol. 118 no. 12
(January, 2005),
pp. 343364, ISSN 00224715 (ISSN: 00224715.) [MR2122959], [mathph/0408060], [Gateway.cgi], [doi] [abs]
 Bakhtin, Y; Mattingly, JC, Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations,
Communications in Contemporary Mathematics, vol. 7 no. 5
(2005),
pp. 553582, World Scientific, ISSN 02191997 (ISSN: 02191997.) [MR2175090], [math.PR/0509166], [doi] [abs]
 Hairer, M; Mattingly, JC, Ergodic properties of highly degenerate 2D stochastic Navier–Stokes equations,
Comptes Rendus Mathematique, vol. 339 no. 12
(December, 2004),
pp. 879882, ISSN 1631073X (ISSN: 1631073X.) [MR2111726], [doi]
 Hairer, M; Mattingly, JC; Pardoux, É, Malliavin calculus for highly degenerate 2D stochastic Navier–Stokes equations,
Comptes Rendus Mathematique, vol. 339 no. 11
(December, 2004),
pp. 793796, ISSN 1631073X [MR2110383], [doi]
 Mattingly, JC; Mattingly, JC; Mattingly, JC, On recent progress for the stochastic Navier Stokes equationsOn recent progress for the stochastic Navier Stokes equationsOn Recent Progress for the Stochastic Navier Stokes Equations,
Journées "Équations aux Dérivées Partielles", vol. XV
(Summer, 2003),
pp. viii+298, Universit\'e de Nantes, Nantes (Held in ForgeslesEaux, June 26, 2003, The
papers are available electronically at
\url{http://www.math.sciences.univnantes.fr/edpa}.) [MR2050586(2004j:00022)], [pdf] [abs]
 Mattingly, JC, Contractivity and Ergodicity of the Random Map $\boldsymbol{\lowercase{x\,\mapsto\,x\theta}}$,
Theory of Probability and Its Applications, vol. 47 no. 2
(2003),
pp. 333333, ISSN 0040585X [repository], [doi]
 Mattingly, JC, The dissipative scale of the stochastics NavierStokes equation: Regularization and analyticity,
Journal of Statistical Physics, vol. 108 no. 56
(December, 2002),
pp. 11571179, ISSN 00224715 (Dedicated to David Ruelle and Yasha Sinai on
the occasion of their 65th birthdays.) [MR2004e:76035], [pdf], [doi] [abs]
 Mattingly, JC, Exponential convergence for the stochastically forced NavierStokes equations and other partially dissipative dynamics,
Communications in Mathematical Physics, vol. 230 no. 3
(November, 2002),
pp. 421462, ISSN 00103616 [MR2004a:76039], [pdf], [doi] [abs]
 Mattingly, JC; Stuart, AM; Higham, DJ, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise,
Stochastic Processes and their Applications, vol. 101 no. 2
(October, 2002),
pp. 185232, ISSN 03044149 [MR2003i:60103], [pdf], [doi] [abs]
 Mattingly, J. C., Contractivity and ergodicity of the random map {$x\mapsto\vert x\theta\vert $},
Teor. Veroyatnost. i Primenen., vol. 47 no. 2
(2002),
pp. 388397 [MR2004f:60148], [pdf] [abs] [author's comments]
 Mattingly, JC; Stuart, AM, Geometric ergodicity of some hypoelliptic diffusions for particle motions,
Markov Processes and Related Fields, vol. 8 no. 2
(2002),
pp. 199214, ISSN 10242953 (Inhomogeneous random systems (CergyPontoise,
2001).) [MR2003g:60101], [pdf] [abs]
 Mattingly, JC; Mattingly, JC, Contractivity and ergodicity of the random map $x\mapstox\theta$, vol. 47 no. 2
(2002),
pp. 388397 [doi]
 E, W; Mattingly, JC, Ergodicity for the NavierStokes equation with degenerate random forcing: Finitedimensional approximation,
Communications on Pure & Applied Mathematics, vol. 54 no. 11
(November, 2001),
pp. 13861402, ISSN 00103640 [MR2002g:76075], [pdf], [doi] [abs]
 E, W; Mattingly, JC; Sinai, Y, Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation,
Communications in Mathematical Physics, vol. 224 no. 1
(November, 2001),
pp. 83106, ISSN 00103616 (Dedicated to Joel L. Lebowitz.) [MR2002m:76024], [pdf], [doi]
 Holmes, PJ; Mattingly, JC; Wittenberg, RW, Lowdimensional models of turbulence or, The dynamics of coherent structures,
in From finite to infinite dimensional dynamical systems (Cambridge, 1995), vol. 19
(2001),
pp. 177215, Kluwer Acad. Publ., Dordrecht [MR2004h:76106], [9789401007320_7], [doi]
 Mattingly, JC, Ergodicity of 2D NavierStokes Equations with¶Random Forcing and Large Viscosity,
Communications in Mathematical Physics, vol. 206 no. 2
(October, 1999),
pp. 273288, ISSN 00103616 [doi]
 Mattingly, JC; Sinai, YG, An elementary proof of the existence and uniqueness theorem for the NavierStokes equations,
Communications in Contemporary Mathematics, vol. 1 no. 4
(1999),
pp. 497516 [MR2000j:35226], [repository] [abs]
 Holmes, PJ; Lumley, JL; Berkooz, G; Mattingly, JC; Wittenberg, RW, Lowdimensional models of coherent structures in turbulence,
Physics Reports, vol. 287 no. 4
(August, 1997),
pp. 337384, ISSN 03701573 [MR98j:76065], [pdf], [doi]
 Mattingly, Jonathan C., Ergodicity of 2D NavierStokes equations with random forcing and large viscosity,
Comm. Math. Phys., vol. 206, no. 2, pp. 273288, 1999
[MR2000k:76040], [pdf]
 Jonathan C. Mattingly, The Stochastic NavierStokes Equation: Energy Estimates and Phase Space Contraction,
PhD Thesis, Princeton University 1998
[ps]
Papers Submitted
 with Bakhtin, Y; Hurth, T; Mattingly, JC, Regularity of invariant densities for 1D systems with random switching,
Nonlinearity, vol. 28 no. 11
(October, 2015),
pp. 37553787, ISSN 09517715 [arXiv:1406.5425], [repository], [doi] [abs]
 with Stephan Huckemann, Ezra Miller, James Nolen, Sticky central limit theorems at isolated hyperbolic planar singularities
(October, 2014) [arXiv:1410.6879] [abs]
 with David P. Herzog, NoiseInduced Stabilization of Planar Flows II
(April, 2014) [arXiv:1404.0955]
 with David P. Herzog, NoiseInduced Stabilization of Planar Flows I
(April, 2014) [arXiv:1404.0957]
 with Sean D. Lawley and Michael C. Reed, Stochastic switching in infinite dimensions with applications to random parabolic PDEs
(2014) [arXiv:1407.2264] [abs]
 with Lawley, SD; Mattingly, JC; Reed, MC, Sensitivity to switching rates in stochastically switched odes,
Communications in Mathematical Sciences, vol. 12 no. 7
(2014),
pp. 13431352, ISSN 15396746 [arXiv:1310.2525], [repository], [doi] [abs]
 Elizabeth Munch, Paul Bendich, Katharine Turner, Sayan Mukherjee, Jonathan Mattingly, John Harer, Probabilistic Fréchet Means and Statistics on Vineyards
(2013) [arXiv:1307.6530] [abs]
Preprints
 Martin Hairer, Jonathan C. Mattingly, Etienne Pardoux, Malliavin calculus and ergodic properties of highly degenerate 2D stochastic NavierStokes equation,
Comptes rendus Mathematique (CRAS), In press
(Summer, 2004) [math.PR/0409057] [abs] [author's comments]


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Mathematics Department
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