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## Publications of Jonathan C. Mattingly    :chronological  alphabetical  combined  bibtex listing:

Papers Published

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 Avanti Athreya, Tiffany Kolba, Propagating Lyapunov functions to prove noise-induced stabilization, Ellectronic Journal of Probability, vol. 17 (November 2, 2012), pp. 1-38 [math/111.1755], [2410], [doi]  [abs]
4. with Mattingly, Jonathan C. and McKinley, Scott A. and Pillai, Natesh S., Geometric ergodicity of a bead--spring pair with stochastic {S}tokes forcing, Stochastic Processes and their Applications, vol. 122 no. 12 (2012), pp. 3953--3979, ISSN 0304-4149 [MR2971721], [0902.4496]  [abs]
5. A. Porporato, P. R. Kramer, M. Cassiani, E. Daly, J. Mattingly, A Local Kinetic Interpretation of Entropy Production through Reversed Diffusion, Phys. Rev. E no. 84 (Fall, 2011) [process.], [doi]  [abs]
6. 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]
7. Katia Koelle, Oliver Ratmann, David Rasmussen, Virginia Pasour, Jonathan Mattingly, A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses, Proc. R. Soc. B (May 4, 2011)  [abs]
8. 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]
9. 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]
10. 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]
11. 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]
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 Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains (August, 2008) [arXiv:0810.2777]  [abs]
14. 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]
15. with Iyer, Gautam and Mattingly, Jonathan, A stochastic-{L}agrangian particle system for the {N}avier-{S}tokes equations, Nonlinearity, vol. 21 no. 11 (2008), pp. 2537--2553, ISSN 0951-7715 [MR2448230 (2009h:76060)], [arXiv:0803.1222]
16. Mattingly, Jonathan C. and Suidan, Toufic M., Transition measures for the stochastic {B}urgers equation, in Integrable systems and random matrices, Contemp. Math., , Integrable systems and random matrices, vol. 458 (2008), pp. 409--418, Amer. Math. Soc., Providence, RI [MR2411921]
17. 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. 313-325
18. Mattingly, Jonathan C. and Suidan, Toufic and Vanden-Eijnden, Eric, Simple systems with anomalous dissipation and energy cascade, Communications in Mathematical Physics, vol. 276 no. 1 (2007), pp. 189--220, ISSN 0010-3616 [MR2342292 (2008m:37135)], [math-ph/0607047]  [abs]
19. Lamba, H. and Mattingly, J. C. and Stuart, A. M., An adaptive {E}uler-{M}aruyama scheme for {SDE}s: convergence and stability, IMA Journal of Numerical Analysis, vol. 27 no. 3 (2007), pp. 479--506, ISSN 0272-4979 [MR2337577], [math.PR/0409057]]
20. Anderson, David F. and Mattingly, Jonathan C. and Nijhout, H. Frederik and Reed, Michael C., Propagation of fluctuations in biochemical systems. {I}. {L}inear {SSC} networks, Bulletin of Mathematical Biology, vol. 69 no. 6 (2007), pp. 1791--1813, ISSN 0092-8240 [MR2329180]
21. Mattingly, Jonathan C. and Suidan, Toufic M. and Vanden-Eijnden, Eric, Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators, Journal of Statistical Physics, vol. 128 no. 5 (2007), pp. 1145--1152, ISSN 0022-4715 [MR2348788], [math-ph/0607047]  [abs]
22. Bakhtin, Yuri and Mattingly, Jonathan C., Malliavin calculus for infinite-dimensional systems with additive noise, Journal of Functional Analysis, vol. 249 no. 2 (2007), pp. 307--353, ISSN 0022-1236 [MR2345335], [math.PR/0610754]  [abs]
23. 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]
24. 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]
25. H. Frederik Nijhout, Michael C. Reed, David F. Anderson, Jonathan C. Mattingly, S. Jill james, and Cornelia M. Ulrich, Long-Range Allosteric Interactions between the Folate and Methionine Cycles Stabilize DNA Methylation Reaction Rate, Epigenetics, Epigenetics, vol. 1 no. 2 (April/May 2006), pp. 81-87
26. 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. 553--582, World Scientific (ISSN: 0219-1997.) [MR2175090], [math.PR/0509166]  [abs]
27. Mattingly, Jonathan C. and Suidan, Toufic M., The small scales of the stochastic Navier-Stokes equations under rough forcing, Journal of Statistical Physics, vol. 118 no. 1-2 (2005), pp. 343--364 (ISSN: 0022-4715.) [MR2122959], [math-ph/0408060]  [abs]
28. Hairer, Martin and Mattingly, Jonathan C., Ergodic properties of highly degenerate 2D stochastic Navier-Stokes equations, Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris, vol. 339 no. 12 (2004), pp. 879--882 (ISSN: 1631-073X.) [MR2111726]
29. 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 (2004), pp. 793-796 [MR2110383]
30. J.C. Mattingly, On Recent Progress for the Stochastic Navier Stokes Equations, Journées "Équations aux Dérivées Partielles" (Forges-les-Eaux, 2003), vol. XV (Summer, 2003), pp. viii+298, Universit\'e de Nantes, Nantes (Held in Forges-les-Eaux, June 2--6, 2003, The papers are available electronically at \url{http://www.math.sciences.univ-nantes.fr/edpa}.) [MR2050586(2004j:00022)], [pdf]  [abs]
31. Mattingly, Jonathan C., The dissipative scale of the stochastics Navier-Stokes equation: regularization and analyticity, J. Statist. Phys., vol. 108 no. 5-6 (2002), pp. 1157--1179 (Dedicated to David Ruelle and Yasha Sinai on the occasion of their 65th birthdays.) [MR2004e:76035], [pdf]  [abs]
32. 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. 388--397 [MR2004f:60148], [pdf]  [abs]
33. Mattingly, J. C. and Stuart, A. M., Geometric ergodicity of some hypo-elliptic diffusions for particle motions, Markov Process. Related Fields, vol. 8 no. 2 (2002), pp. 199--214 (Inhomogeneous random systems (Cergy-Pontoise, 2001).) [MR2003g:60101], [pdf]  [abs]
34. 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]
35. 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]
36. E, Weinan and Mattingly, Jonathan C., Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation, Comm. Pure Appl. Math., vol. 54 no. 11 (2001), pp. 1386--1402 [MR2002g:76075], [pdf]  [abs]
37. Holmes, P. J. and Mattingly, J. C. and Wittenberg, R. W., Low-dimensional 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. 177--215, 2001, Kluwer Acad. Publ., Dordrecht, From finite to infinite dimensional dynamical systems (Cambridge, 1995), vol. 19 (2001), pp. 177--215, Kluwer Acad. Publ., Dordrecht [MR2004h:76106]
38. 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]
39. Mattingly, Jonathan C., Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity, Comm. Math. Phys., vol. 206, no. 2, pp. 273--288, 1999 [MR2000k:76040], [pdf]
40. Mattingly, J. C. and Sinai, Ya. G., An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations, Commun. Contemp. Math., vol. 1, no. 4, pp. 497--516, 1999 [MR2000j:35226], [pdf]  [abs]
41. Jonathan C. Mattingly, The Stochastic Navier-Stokes Equation: Energy Estimates and Phase Space Contraction, PhD Thesis, Princeton University 1998 [ps]
42. Holmes, Philip J. and Lumley, John L. and Berkooz, Gal and Mattingly, Jonathan C. and Wittenberg, Ralf W., Low-dimensional models of coherent structures in turbulence, Phys. Rep., vol. 287, no. 4, pp. 337--384, 1997 [MR98j:76065], [pdf]

Papers Submitted

1. with Stephan Huckemann, Ezra Miller, James Nolen, Sticky central limit theorems at isolated hyperbolic planar singularities (October, 2014) [arXiv:1410.6879]  [abs]
2. with David P. Herzog, Noise-Induced Stabilization of Planar Flows II (April, 2014) [arXiv:1404.0955]
3. with David P. Herzog, Noise-Induced Stabilization of Planar Flows I (April, 2014) [arXiv:1404.0957]
4. with Yuri Bakhtin, Tobias Hurth, Regularity of invariant densities for 1D-systems with random switching (2014) [arXiv:1406.5425]  [abs]
5. with Sean D. Lawley and Michael C. Reed, Stochastic switching in infinite dimensions with applications to random parabolic PDEs (2014) [arXiv:1407.2264]  [abs]
6. with Sean D. Lawley and Michael C. Reed, Sensitivity to switching rates in stochastically switched ODEs (2014) [arXiv:1310.2525]  [abs]
7. Elizabeth Munch, Paul Bendich, Katharine Turner, Sayan Mukherjee, Jonathan Mattingly, John Harer, Probabilistic Fréchet Means and Statistics on Vineyards (2013) [arXiv:1307.6530]  [abs]
8. with Matthias Heymann, Stephen W. Teitsworth, Rare Transition Events in Nonequilibrium Systems with State-Dependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices (2010) [1008.4037]  [abs]

Preprints

1. with Christy Vaughn, Redistricting and the Will of the People (October, 2014) [pdf]  [abs]
2. Martin Hairer, Jonathan C. Mattingly, Etienne Pardoux, Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier--Stokes equation, Comptes rendus Mathematique (CRAS), In press (Summer, 2004) [math.PR/0409057]  [abs]

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