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Research Interests for Jonathan C. Mattingly

Research Interests: Applied mathematics, Probability, Ergodic Theory, Stochastic partial differential equations, Stochastic dynamical systems, Stochastic Numerical methods, Fluids

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
  1. JC Mattingly and E Pardoux, Invariant measure selection by noise. An example, Discrete and Continuous Dynamical Systems, vol. 34 no. 10 (2014), pp. 4223-4257, ISSN 1078-0947 [arXiv:1403.3593], [repository], [doi[abs]
  2. 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. 2238-2258, ISSN 1050-5164 [arXiv:1202.4267], [12-AAP899], [doi[abs]
  3. 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. 881-930 [1003.4306], [1003.4306v4], [doi[abs]
  4. with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains (August, 2008) [arXiv:0810.2777[abs]
  5. with David P. Herzog, Noise-Induced Stabilization of Planar Flows II (Submitted, April, 2014) [arXiv:1404.0955]
  6. 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. 301-318, ISSN 1539-6746 [0906.3475], [repository[abs]
  7. 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. 658-738, ISSN 1083-6489 [arXiv:0808.1361], [repository[abs]
  8. with Martin Hairer, Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations, Annals of Probability no. 6 (2008), pp. 993-1032 [MR2478676], [math.PR/0602479[abs]
  9. with David P. Herzog, Noise-Induced Stabilization of Planar Flows I (Submitted, April, 2014) [arXiv:1404.0957]
  10. 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. 223-259, ISSN 0178-8051 [MR2531551], [0902.4495], [repository], [doi[abs]
  11. 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. 3755-3787, ISSN 0951-7715 [arXiv:1406.5425], [repository], [doi[abs]
  12. M Hairer and JC Mattingly, Slow energy dissipation in anharmonic oscillator chains, Communications on Pure and Applied Mathematics, vol. 62 no. 8 (2008), pp. 999-1032, ISSN 0010-3640 [MR2531551], [arXiv:0712.3884], [doi[abs]
  13. 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]
  14. with JC Mattingly, AM Stuart and MV Tretyakov, Convergence of numerical time-averaging and stationary measures via Poisson equations, SIAM Journal on Numerical Analysis, vol. 48 no. 2 (2010), pp. 552-577, ISSN 0036-1429 [MR2669996], [0908.4450], [repository], [doi[abs]
  15. 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. 185-232, ISSN 0304-4149 [MR2003i:60103], [pdf], [doi[abs]
  16. with JC Mattingly and C Vaughn, Redistricting and the Will of the People, arxiv (Preprint, October, 2014) [1410.8796v1[abs]
  17. JC Mattingly and É Pardoux, Malliavin calculus for the stochastic 2D Navier-Stokes equation, Communications on Pure and Applied Mathematics, vol. 59 no. 12 (December, 2006), pp. 1742-1790, ISSN 0010-3640 [math.PR/0407215], [doi[abs]
  18. JC Mattingly, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics, Communications in Mathematical Physics, vol. 230 no. 3 (November, 2002), pp. 421-462, ISSN 0010-3616 [MR2004a:76039], [pdf], [doi[abs]
  19. M Hairer and JC Mattingly, Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing, Annals of Mathematics, vol. 164 no. 3 (November, 2006), pp. 993-1032, ISSN 0003-486X [math.PR/0406087[abs]
  20. 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. 83-106, ISSN 0010-3616 (Dedicated to Joel L. Lebowitz.) [MR2002m:76024], [pdf], [doi]
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