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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

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. Jonathan C. Mattingly and Etienne Pardoux, Invariant measure selection by noise: An Example, Discrete and Continuous Dynamical Systems. Series A, vol. 34 no. 10 (2014), pp. 4223--4257 [arXiv:1403.3593[abs]
  2. 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, Ann. Appl. Probab., vol. 23 no. 6 (2013), pp. 2238--2258 [arXiv:1202.4267[abs]
  3. 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]
  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 David Anderson, A weak trapezoidal method for a class of stochastic differential equations, Communications in Mathematical Sciences, vol. 9 no. 1 (March, 2011), pp. 301 - 318 [0906.3475[abs]
  7. with Martin Hairer, A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs, EJP, vol. 16 no. 23 (2011), pp. 658–738 [arXiv:0808.1361], [getdoc.php]
  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 Martin Hairer, Michael Scheutzow, Asymptotic coupling and a weak form of Harris' theorem with applications to stochastic delay equations, Probability Theory and related Fields (2009) [MR2531551], [0902.4495[abs]
  11. with Yuri Bakhtin, Tobias Hurth, Regularity of invariant densities for 1D-systems with random switching (Submitted, 2014) [arXiv:1406.5425[abs]
  12. 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. 999--1032, ISSN 0010-3640 [MR2531551], [arXiv:0712.3884[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 Mattingly, Jonathan C. and Stuart, Andrew M. and Tretyakov, M. V., Convergence of numerical time-averaging and stationary measures via {P}oisson equations, SIAM Journal on Numerical Analysis, vol. 48 no. 2 (2010), pp. 552--577, ISSN 0036-1429 [MR2669996], [0908.4450], [090770527[abs]
  15. Mattingly, J. C. and Stuart, A. M. and Higham, D. J., Ergodicity for {SDE}s and approximations: locally Lipschitz vector fields and degenerate noise, Stochastic Process. Appl., vol. 101 no. 2 (2002), pp. 185--232 [MR2003i:60103], [pdf[abs]
  16. with Christy Vaughn, Redistricting and the Will of the People (Preprint, October, 2014) [pdf[abs]
  17. Jonathan C. Mattingly, Etienne 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 [math.PR/0407215[abs]
  18. J.C. Mattingly, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics, Comm. Math. Phys., vol. 230 no. 3 (2002), pp. 421--462 [MR2004a:76039], [pdf]
  19. Martin Hairer, J.C. Mattingly, Ergodicity of the 2D Navier-Stokes Equations with Degenerate Stochastic Forcing, Annals of Mathematics, vol. 164 no. 3 (November, 2006) [math.PR/0406087[abs]
  20. W. E, J.C. Mattingly, Ya Sinai, Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation, Comm. Math. Phys., vol. 224 no. 1 (2001), pp. 83--106 (Dedicated to Joel L. Lebowitz.) [MR2002m:76024], [pdf]
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