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

Papers Published

1. A. Porporato, P. R. Kramer, M. Cassiani, E. Daly, J. Mattingly. "A Local Kinetic Interpretation of Entropy Production through Reversed Diffusion." Phys. Rev. E 84 (Fall, 2011). [process.], [doi]  [abs]
2. 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]
3. 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]
4. with David Anderson. "A weak trapezoidal method for a class of stochastic differential equations." Communications in Mathematical Sciences 9.1 (March, 2011): 301 - 318. [0906.3475]  [abs]
5. with Martin Hairer. "A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs." EJP 16.23 (2011): 658–738. [arXiv:0808.1361], [getdoc.php]
6. 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 48.2 (2010): 552--577. [MR2669996], [0908.4450], [090770527]  [abs]
7. 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]
8. Hairer, Martin and Mattingly, Jonathan C.. "Slow energy dissipation in anharmonic oscillator chains." Communications on Pure and Applied Mathematics 62.8 (2008): 999--1032. [MR2531551], [arXiv:0712.3884]  [abs]
9. with Martin Hairer. "Yet another look at Harris' ergodic theorem for Markov chains." (August, 2008). [arXiv:0810.2777]  [abs]
10. with Martin Hairer. "Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations." Annals of Probability 6 (2008): 993--1032. [MR2478676], [math.PR/0602479]  [abs]
11. with Iyer, Gautam and Mattingly, Jonathan. "A stochastic-{L}agrangian particle system for the {N}avier-{S}tokes equations." Nonlinearity 21.11 (2008): 2537--2553. [MR2448230 (2009h:76060)], [arXiv:0803.1222]
12. Mattingly, Jonathan C. and Suidan, Toufic M.. "Transition measures for the stochastic {B}urgers equation." , Integrable systems and random matricesIntegrable systems and random matrices Contemp. Math. 458 (2008): 409--418. [MR2411921]
13. David Anderson and Jonathan C. Mattingly. "Propagation of fluctuations in biochemical systems, II: nonlinear chains." IET Systems Biology 1.6 (November, 2007): 313-325.
14. Mattingly, Jonathan C. and Suidan, Toufic and Vanden-Eijnden, Eric. "Simple systems with anomalous dissipation and energy cascade." Communications in Mathematical Physics 276.1 (2007): 189--220. [MR2342292 (2008m:37135)], [math-ph/0607047]  [abs]
15. 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 27.3 (2007): 479--506. [MR2337577], [math.PR/0409057]]  [author's comments]
16. 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 69.6 (2007): 1791--1813. [MR2329180]
17. 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 128.5 (2007): 1145--1152. [MR2348788], [math-ph/0607047]  [abs]
18. Bakhtin, Yuri and Mattingly, Jonathan C.. "Malliavin calculus for infinite-dimensional systems with additive noise." Journal of Functional Analysis 249.2 (2007): 307--353. [MR2345335], [math.PR/0610754]  [abs]
19. Jonathan C. Mattingly, Etienne Pardoux. "Malliavin calculus for the Stochastic 2D Navier Stokes Equation." Communications on Pure and Applied Mathematics 59.12 (December, 2006): 1742 - 1790. [math.PR/0407215]  [abs]
20. Martin Hairer, J.C. Mattingly. "Ergodicity of the 2D Navier-Stokes Equations with Degenerate Stochastic Forcing." Annals of Mathematics 164.3 (November, 2006). [math.PR/0406087]  [abs]
21. 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 1.2 (April/May 2006): 81-87.
22. Bakhtin, Yuri and Mattingly, Jonathan C.. "Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations." Communications in Contemporary Mathematics 7.5 (2005): 553--582. (ISSN: 0219-1997) [MR2175090], [math.PR/0509166]  [abs]
23. Mattingly, Jonathan C. and Suidan, Toufic M.. "The small scales of the stochastic Navier-Stokes equations under rough forcing." Journal of Statistical Physics 118.1-2 (2005): 343--364. (ISSN: 0022-4715) [MR2122959], [math-ph/0408060]  [abs]
24. 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 339.12 (2004): 879--882. (ISSN: 1631-073X) [MR2111726]
25. Martin Hairer, Jonathan C. Mattingly and Étienne Pardoux. "Malliavin calculus for highly degenerate 2D stochastic Navier–Stokes equations." Comptes Rendus Mathematique 339.11 (2004): 793-796. [MR2110383]
26. J.C. Mattingly. "On Recent Progress for the Stochastic Navier Stokes Equations." Journées "Équations aux Dérivées Partielles" (Forges-les-Eaux, 2003) XV (Summer, 2003): viii+298. (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]
27. Mattingly, Jonathan C.. "The dissipative scale of the stochastics Navier-Stokes equation: regularization and analyticity." J. Statist. Phys. 108.5-6 (2002): 1157--1179. (Dedicated to David Ruelle and Yasha Sinai on the occasion of their 65th birthdays) [MR2004e:76035], [pdf]  [abs]
28. Mattingly, J. C.. "Contractivity and ergodicity of the random map {$x\mapsto\vert x-\theta\vert $}." Teor. Veroyatnost. i Primenen. 47.2 (2002): 388--397. [MR2004f:60148], [pdf]  [abs] [author's comments]
29. Mattingly, J. C. and Stuart, A. M.. "Geometric ergodicity of some hypo-elliptic diffusions for particle motions." Markov Process. Related Fields 8.2 (2002): 199--214. (Inhomogeneous random systems (Cergy-Pontoise, 2001)) [MR2003g:60101], [pdf]  [abs]
30. 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. 101.2 (2002): 185--232. [MR2003i:60103], [pdf]  [abs]
31. J.C. Mattingly. "Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics." Comm. Math. Phys. 230.3 (2002): 421--462. [MR2004a:76039], [pdf]
32. E, Weinan and Mattingly, Jonathan C.. "Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation." Comm. Pure Appl. Math. 54.11 (2001): 1386--1402. [MR2002g:76075], [pdf]  [abs]
33. Holmes, P. J. and Mattingly, J. C. and Wittenberg, R. W.. "Low-dimensional models of turbulence or, The dynamics of coherent structures." 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)From finite to infinite dimensional dynamical systems (Cambridge, 1995) 19 (2001): 177--215. [MR2004h:76106]
34. W. E, J.C. Mattingly, Ya Sinai. "Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation." Comm. Math. Phys. 224.1 (2001): 83--106. (Dedicated to Joel L. Lebowitz) [MR2002m:76024], [pdf]
35. 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]
36. 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]
37. Jonathan C. Mattingly. "The Stochastic Navier-Stokes Equation: Energy Estimates and Phase Space Contraction." PhD Thesis, Princeton University 1998 (). [ps]
38. 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 Accepted

1. with Scott A. McKinley, Natesh S. Pillai. "Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing."   (2009). [0902.4496]  [abs]

Papers Submitted

1. with Avanti Athreya, Tiffany Kolba. "Propagating lyapunov functions to prove noise–induced stabilization."   (November, 2011). [math/111.1755]  [abs]
2. with Ben Cooke, Scott A. McKinley, Scott C. Schmidler. "Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential."   (April, 2011). [math/1104.3842]  [abs]
3. 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. 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]