Math @ Duke

Papers Published
 DP Herzog and JC Mattingly, Noiseinduced stabilization of planar flows ii,
Electronic Journal of Probability, vol. 20
(October, 2015) [doi] [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 [doi]
 S Huckemann, J Mattingly, E Miller and J Nolen, Sticky central limit theorems at isolated hyperbolic planar singularities,
Electronic Journal of Probability, vol. 20
(July, 2015) [doi]
 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 [doi]
 Jonathan C. Mattingly and Etienne 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], [doi] [abs]
 Thomas Hotz, Sean Skwerer, Stephan Huckemann, Huiling Le, J. S. Marron, Jonathan C. Mattingly, Ezra Miller, James Nolen, Megan Owen, Vic Patrangenaru, 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]
 with Avanti Athreya, Tiffany Kolba, Propagating lyapunov functions to prove noiseinduced stabilization,
Electronic Journal of Probability, vol. 17
(November 2, 2012),
pp. 138, ISSN 10836489 [math/111.1755], [2410], [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 Mattingly, Jonathan C. and McKinley, Scott A. and Pillai, Natesh S., 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], [doi] [abs]
 A. Porporato, P. R. Kramer, M. Cassiani, E. Daly, 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]
 with Natesh S. Pillai, Andrew M. Stuart, Diffusion Limits of the Random Walk Metropolis Algorithm in High Dimensions,
Annals of Applied Probability
(June, 2011) [1003.4306] [abs]
 Katia Koelle, Oliver Ratmann, David Rasmussen, Virginia Pasour, Jonathan 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 [doi] [abs]
 with David Anderson, 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] [abs]
 with Martin Hairer, Michael 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], [doi] [abs]
 with Martin Hairer, 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], [getdoc.php] [abs]
 with Mattingly, Jonathan C. and Stuart, Andrew M. and Tretyakov, M. V., 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], [090770527], [doi] [abs]
 Hairer, Martin and Mattingly, Jonathan C., 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]
 with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains
(August, 2008) [arXiv:0810.2777] [abs]
 Mattingly, Jonathan C. and Suidan, Toufic M., 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 [MR2411921], [Gateway.cgi]
 with Iyer, Gautam and Mattingly, Jonathan, 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]
 David Anderson and Jonathan C. Mattingly, Propagation of fluctuations in biochemical systems, II: nonlinear chains,
IET Systems Biology, vol. 1 no. 6
(November, 2007),
pp. 313325, ISSN 17518849 [doi]
 Anderson, David F. and Mattingly, Jonathan C. and Nijhout, H. Frederik and Reed, Michael C., 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]
 Lamba, H. and Mattingly, J. C. and Stuart, A. M., 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, Jonathan C. and Suidan, Toufic and VandenEijnden, Eric, 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, Yuri and Mattingly, Jonathan C., 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, Jonathan C. and Suidan, Toufic M. and VandenEijnden, Eric, 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]
 Jonathan C. Mattingly, Etienne 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]
 Martin Hairer, J.C. 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]
 Mattingly, Jonathan C. and Suidan, Toufic M., 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, Yuri and Mattingly, Jonathan C., 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, Martin and Mattingly, Jonathan C., 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]
 Martin Hairer, Jonathan C. Mattingly and Étienne 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]
 J.C. 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 [doi]
 Mattingly, Jonathan C., 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]
 J.C. 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]
 Mattingly, J. C. and Stuart, A. M. and Higham, D. J., 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, J. C. and Stuart, A. M., 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]
 E, Weinan and Mattingly, Jonathan C., 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, J.C. Mattingly, Ya 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]
 Holmes, P. J. and Mattingly, J. C. and Wittenberg, R. W., Lowdimensional models of turbulence or, The dynamics of coherent structures,
in From finite to infinite dimensional dynamical systems (Cambridge, 1995),
From finite to infinite dimensional dynamical systems (Cambridge, 1995), vol. 19, pp. 177215, 2001, Kluwer Acad. Publ., Dordrecht, From finite to infinite dimensional dynamical systems (Cambridge, 1995), 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]
 Mattingly, J. C. and Sinai, Ya. G., 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], [pdf] [abs]
 Holmes, Philip J. and Lumley, John L. and Berkooz, Gal and Mattingly, Jonathan C. and Wittenberg, Ralf W., 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 Yuri Bakhtin, Tobias Hurth, Regularity of invariant densities for 1D systems with random switching,
Nonlinearity, vol. 28 no. 11
(October, 2015),
pp. 37553787, ISSN 09517715 [arXiv:1406.5425], [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 Sean D. Lawley and Michael C. 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], [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 Matthias Heymann, Stephen W. Teitsworth, Rare Transition Events in Nonequilibrium Systems with StateDependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices
(2010) [1008.4037] [abs]
Preprints
 with Christy Vaughn, Redistricting and the Will of the People
(October, 2014) [pdf] [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]


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