Math @ Duke

Research Interests for Jonathan C. Mattingly
Research Interests: Applied mathematics, Probability, Ergodic Theory, Stochastic partial differential equations, Stochastic dynamical systems, Stochastic Numerical methods, Fluids
 Keywords:
 Differential equations, Nonlinear, Ergodic theory, Evolution, Fluid mechanics, Folic Acid, Invariant measures, Lyapunov functions, Malliavin calculus, Mixing, Models, Biological, Nonequilibrium statistical mechanics, Nonlinear Dynamics, Probability Theory, Random dynamical systems, Stochastic analysis, Stochastic differential equations, Stochastic partial differential equations, Stochastic Processes, Turbulence
 Areas of Interest:
Ergodic theory Truly infinite dimensional behabior in SPDEs Scaling limited of algorithems used in simulation and data analysis Probabilistic algorithms for large data Stabilization of dynamics my noise scaling limits of stochastic algorithms
 Representative Publications
 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], [repository], [doi] [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]
 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 Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains
(August, 2008) [arXiv:0810.2777] [abs]
 with David P. Herzog, NoiseInduced Stabilization of Planar Flows II
(Submitted, April, 2014) [arXiv:1404.0955]
 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], [repository] [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], [repository] [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]
 with David P. Herzog, NoiseInduced Stabilization of Planar Flows I
(Submitted, April, 2014) [arXiv:1404.0957]
 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], [repository], [doi] [abs]
 with Y Bakhtin, T Hurth and JC Mattingly, Regularity of invariant densities for 1D systems with random switching,
Nonlinearity, vol. 28 no. 11
(October, Submitted, 2015),
pp. 37553787, ISSN 09517715 [arXiv:1406.5425], [repository], [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]
 with Sean D. Lawley and Michael C. Reed, Stochastic switching in infinite dimensions with applications to random parabolic PDEs
(Submitted, 2014) [arXiv:1407.2264] [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], [repository], [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]
 with JC Mattingly and C Vaughn, Redistricting and the Will of the People,
arxiv
(Preprint, October, 2014) [1410.8796v1] [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]
 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]
 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]
 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]


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