Publications of Jonathan C. Mattingly     :recent first  combined  bibtex listing:

Papers Published

1. 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]
2. Jonathan C. Mattingly, The Stochastic Navier-Stokes Equation: Energy Estimates and Phase Space Contraction, PhD Thesis, Princeton University 1998 [ps]
3. 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]
4. 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]
5. 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]
6. 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]
7. 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]
8. 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]
9. 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]
10. 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]
11. 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]
12. 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] [author's comments]
13. 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]
14. 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]
15. 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]
16. 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]
17. 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]
18. 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
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. 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]
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. 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]
24. 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]]  [author's comments]
25. 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]
26. 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
27. 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]
28. 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]
29. 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]
30. 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]

Papers Accepted

1. with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains (August, 2008) [arXiv:0810.2777]  [abs]
2. with Martin Hairer, Michael Scheutzow, Asymptotic coupling and a weak form of Harris' theorem with applications to stochastic delay equations (2009) [0902.4495]  [abs]

Papers Submitted

1. with Martin Hairer, A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs (2008) [arXiv:0808.1361]
2. with Scott A. McKinley, Natesh S. Pillai, Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing (2009) [0902.4496v1]  [abs]
3. with David Anderson, A weak trapezoidal method for a class of stochastic differential equations (2009) [0906.3475]  [abs]
4. with Andrew M. Stuart and M.V. Tretyakov, Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations (2009) [0908.4450v2]  [abs]

Preprints

1. 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] [author's comments]