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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

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
  1. Mattingly, JC; Pardoux, E, 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. 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. 2238-2258, ISSN 1050-5164 [arXiv:1202.4267], [12-AAP899], [doi[abs]
  3. with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains (August, 2008) [arXiv:0810.2777[abs]
  4. with David P. Herzog, Noise-Induced Stabilization of Planar Flows II (Submitted, April, 2014) [arXiv:1404.0955]
  5. 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. 301-318, ISSN 1539-6746 [0906.3475], [repository[abs]
  6. 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. 658-738, ISSN 1083-6489 [arXiv:0808.1361], [repository[abs]
  7. with Hairer, M; Mattingly, JC; Martin Hairer, , Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equationsSpectral 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]
  8. with David P. Herzog, Noise-Induced Stabilization of Planar Flows I (Submitted, April, 2014) [arXiv:1404.0957]
  9. 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. 223-259, ISSN 0178-8051 [MR2531551], [0902.4495], [repository], [doi[abs]
  10. with Bakhtin, Y; Hurth, T; Mattingly, JC, 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]
  11. Hairer, M; Mattingly, JC, Slow energy dissipation in anharmonic oscillator chains, Communications on Pure & Applied Mathematics, vol. 62 no. 8 (2008), pp. 999-1032, ISSN 0010-3640 [MR2531551], [arXiv:0712.3884], [doi[abs]
  12. 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]
  13. with Mattingly, JC; Stuart, AM; Tretyakov, MV, 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]
  14. 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. 185-232, ISSN 0304-4149 [MR2003i:60103], [pdf], [doi[abs]
  15. Mattingly, JC; Pardoux, É, Malliavin calculus for the stochastic 2D Navier-Stokes equation, Communications on Pure & Applied Mathematics, vol. 59 no. 12 (December, 2006), pp. 1742-1790, ISSN 0010-3640 [math.PR/0407215], [doi[abs]
  16. Mattingly, JC, 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]
  17. Hairer, M; Mattingly, JC, 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]
  18. 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. 83-106, ISSN 0010-3616 (Dedicated to Joel L. Lebowitz.) [MR2002m:76024], [pdf], [doi]

 

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