Math @ Duke

Papers Published
 NE GlattHoltz, JC Mattingly and G Richards, On Unique Ergodicity in Nonlinear Stochastic Partial Differential
Equations,
arxiv
(December, 2015) [1512.04126v1] [abs]
 JE Johndrow, JC Mattingly, S Mukherjee and D Dunson, Approximations of Markov Chains and Bayesian Inference,
arxiv
(August, 2015) [1508.03387v2] [abs]
 DP Herzog and JC Mattingly, A practical criterion for positivity of transition densities,
Nonlinearity, vol. 28 no. 8
(August, 2015),
pp. 28232845, ISSN 09517715 [DukeSpace], [doi]
 S Luo and JC Mattingly, Scaling limits of a model for selection at two scales,
arxiv
(July, 2015) [1507.00397v1] [abs]
 S Huckemann, J Mattingly, E Miller and J Nolen, Sticky central limit theorems at isolated hyperbolic planar singularities,
Electronic Journal of Probability, vol. 20
(January, 2015) [DukeSpace], [doi]
 DP Herzog and JC Mattingly, NoiseInduced Stabilization of Planar Flows II,
Electronic Journal of Probability, vol. 20
(January, 2015) [DukeSpace], [doi] [abs]
 SD Lawley, JC Mattingly and MC Reed, 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 [DukeSpace], [doi]
 JC Mattingly and E Pardoux, Invariant measure selection by noise. An example,
Discrete and Continuous Dynamical Systems, vol. 34 no. 10
(2014),
pp. 42234257, ISSN 10780947 [arXiv:1403.3593], [DukeSpace], [doi] [abs]
 E Munch, K Turner, P Bendich, S Mukherjee, J Mattingly and J Harer, Probabilistic Fréchet Means for Time Varying Persistence Diagrams,
arxiv
(July, 2013) [1307.6530v3] [abs]
 T Hotz, S Huckemann, H Le, JS Marron, JC Mattingly, E Miller, J Nolen, M Owen, V Patrangenaru and S Skwerer, Sticky central limit theorems on open books,
The Annals of Applied Probability, vol. 23 no. 6
(2013),
pp. 22382258, ISSN 10505164 [arXiv:1202.4267], [12AAP899], [doi] [abs]
 S Luo, M Reed, JC Mattingly and K Koelle, The impact of host immune status on the withinhost and population dynamics of antigenic immune escape.,
J R Soc Interface, vol. 9 no. 75
(October, 2012),
pp. 26032613 [22572027], [doi] [abs]
 with JC Mattingly, SA McKinley and NS Pillai, 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], [DukeSpace], [doi] [abs]
 with A Athreyaz, T Kolba and JC Mattingly, Propagating lyapunov functions to prove noiseinduced stabilization,
Electronic Journal of Probability, vol. 17
(November 2, 2012),
pp. 138, ISSN 10836489 [math/111.1755], [DukeSpace], [doi] [abs]
 A Porporato, PR Kramer, M Cassiani, E Daly and J Mattingly, Local kinetic interpretation of entropy production through reversed diffusion.,
Phys Rev E Stat Nonlin Soft Matter Phys, vol. 84 no. 4 Pt 1
(Fall, 2011),
pp. 041142 [22181122], [doi] [abs]
 K Koelle, O Ratmann, DA Rasmussen, V Pasour and J Mattingly, A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses,
Proceedings of the Royal Society B: Biological Sciences, vol. 278 no. 1725
(May 4, 2011),
pp. 37233730, ISSN 09628452 [DukeSpace], [doi] [abs]
 with M Hairer, JC Mattingly and M Scheutzow, 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], [DukeSpace], [doi] [abs]
 with DF Anderson and JC Mattingly, 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], [DukeSpace] [abs]
 with M Hairer and JC Mattingly, 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], [DukeSpace] [abs]
 with JC Mattingly, NS Pillai and AM Stuart, Diffusion limits of the random walk Metropolis algorithm in high
dimensions,
Annals of Applied Probability, vol. 22 no. 3
(June, 2011),
pp. 881930 [1003.4306], [1003.4306v4], [doi] [abs]
 with JC Mattingly, AM Stuart and MV Tretyakov, 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], [DukeSpace], [doi] [abs]
 M Hairer and JC Mattingly, Slow energy dissipation in anharmonic oscillator chains,
Communications on Pure and Applied Mathematics, vol. 62 no. 8
(2008),
pp. 9991032, ISSN 00103640 [MR2531551], [arXiv:0712.3884], [doi] [abs]
 M Hairer and JC Mattingly, Yet another look at Harris' ergodic theorem for Markov chains,
arxiv
(October, 2008) [0810.2777v1] [abs]
 with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains
(August, 2008) [arXiv:0810.2777] [abs]
 JC Mattingly and TM Suidan, Transition measures for the stochastic Burgers equation,
in Integrable systems and random matrices, Contemp. Math.,
INTEGRABLE SYSTEMS AND RANDOM MATRICES: IN HONOR OF PERCY DEIFT, vol. 458
(2008),
pp. 409418, Amer. Math. Soc., Providence, RI, ISSN 02714132, ISBN 9780821842409 [MR2411921], [Gateway.cgi]
 with G Iyer and J Mattingly, 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 Martin Hairer, Spectral gaps in Wasserstein distances and the 2D stochastic NavierStokes equations,
Annals of Probability no. 6
(2008),
pp. 9931032 [MR2478676], [math.PR/0602479] [abs]
 JC Mattingly and DF Anderson, Propagation of fluctuations in biochemical systems, II: nonlinear chains,
IET Systems Biology, vol. 1 no. 6
(November, 2007),
pp. 313325, ISSN 17518849 [DukeSpace], [doi]
 DF Anderson, JC Mattingly, HF Nijhout and MC Reed, Propagation of fluctuations in biochemical systems, I: linear SSC networks.,
Bull Math Biol, vol. 69 no. 6
(August, 2007),
pp. 17911813, ISSN 00928240 [MR2329180], [17457656], [doi] [abs]
 H Lamba, JC Mattingly and AM Stuart, 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]
 JC Mattingly, T Suidan and E VandenEijnden, 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]
 Y Bakhtin and JC Mattingly, 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]
 JC Mattingly, TM Suidan and E VandenEijnden, 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]
 HF Nijhout, MC Reed, DF Anderson, JC Mattingly, SJ James and CM Ulrich, Longrange allosteric interactions between the folate and methionine cycles stabilize DNA methylation reaction rate.,
Epigenetics, vol. 1 no. 2
(April/May 2006),
pp. 8187, ISSN 15592294 [17998813] [abs]
 JC Mattingly and É Pardoux, Malliavin calculus for the stochastic 2D NavierStokes equation,
Communications on Pure and Applied Mathematics, vol. 59 no. 12
(December, 2006),
pp. 17421790, ISSN 00103640 [math.PR/0407215], [doi] [abs]
 M Hairer and JC Mattingly, 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]
 JC Mattingly and TM Suidan, 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]
 Y Bakhtin and JC Mattingly, 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]
 M Hairer and JC Mattingly, 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]
 M Hairer, JC Mattingly and É Pardoux, 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]
 M Hairer, JC Mattingly and E Pardoux, Malliavin calculus and ergodic properties of highly degenerate 2D
stochastic NavierStokes equation,
arxiv
(September, 2004) [0409057v1] [abs]
 JC Mattingly, On 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]
 JC Mattingly, 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 [DukeSpace], [doi]
 JC Mattingly, 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]
 JC Mattingly, 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]
 JC Mattingly, AM Stuart and DJ Higham, 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]
 JC Mattingly and AM Stuart, 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]
 W E and JC Mattingly, Ergodicity for the NavierStokes equation with degenerate random forcing: Finitedimensional approximation,
Communications on Pure and Applied Mathematics, vol. 54 no. 11
(November, 2001),
pp. 13861402, ISSN 00103640 [MR2002g:76075], [pdf], [doi] [abs]
 W E, JC Mattingly and Y Sinai, 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]
 PJ Holmes, JC Mattingly and RW Wittenberg, Lowdimensional models of turbulence or, The dynamics of coherent structures,
in From finite to infinite dimensional dynamical systems (Cambridge, 1995),
manual, vol. 19
(2001),
pp. 177215, Kluwer Acad. Publ., Dordrecht [MR2004h:76106], [9789401007320_7], [doi]
 JC Mattingly, 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]
 JC Mattingly and YG Sinai, 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], [DukeSpace] [abs]
 PJ Holmes, JL Lumley, G Berkooz, JC Mattingly and RW Wittenberg, 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 Y Bakhtin, T Hurth and JC Mattingly, Regularity of invariant densities for 1D systems with random switching,
Nonlinearity, vol. 28 no. 11
(October, 2015),
pp. 37553787, ISSN 09517715 [arXiv:1406.5425], [DukeSpace], [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 SD Lawley, JC Mattingly and MC Reed, Sensitivity to switching rates in stochastically switched odes,
Communications in Mathematical Sciences, vol. 12 no. 7
(2014),
pp. 13431352, ISSN 15396746 [arXiv:1310.2525], [DukeSpace], [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]
 with M Heymann, SW Teitsworth and JC Mattingly, Rare Transition Events in Nonequilibrium Systems with StateDependent
Noise: Application to Stochastic Current Switching in Semiconductor
Superlattices,
arxiv
(August, 2010) [1008.4037], [1008.4037v2] [abs]
Preprints
 with JC Mattingly and C Vaughn, Redistricting and the Will of the People,
arxiv
(October, 2014) [1410.8796v1] [abs]
 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]


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

