Publications of Jonathan C. Mattingly
Papers Published
- Earle, G; Mattingly, JC, Convergence of stratified MCMC sampling of non-reversible dynamics,
Stochastics and Partial Differential Equations: Analysis and Computations
(January, 2024)
- Autry, E; Carter, D; Herschlag, GJ; Hunter, Z; Mattingly, JC, METROPOLIZED FOREST RECOMBINATION FOR MONTE CARLO SAMPLING OF GRAPH PARTITIONS,
SIAM Journal on Applied Mathematics, vol. 83 no. 4
(August, 2023),
pp. 1366-1391, Society for Industrial & Applied Mathematics (SIAM)
- Herzog, DP; Mattingly, JC; Nguyen, HD, Gibbsian dynamics and the generalized Langevin equation,
Electronic Journal of Probability, vol. 28
(January, 2023)
- Zhao, Z; Hettle, C; Gupta, S; Mattingly, JC; Randall, D; Herschlag, GJ, Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan,
ACM International Conference Proceeding Series
(October, 2022), ISBN 9781450394772
- Mattingly, JC; Romito, M; Su, L, The Gaussian structure of the singular stochastic Burgers equation,
Forum of Mathematics, Sigma, vol. 10
(September, 2022), Cambridge University Press (CUP)
- Li, L; Lu, J; Mattingly, JC; Wang, L, Numerical Methods For Stochastic Differential Equations Based On Gaussian Mixture,
Communications in Mathematical Sciences, vol. 19 no. 6
(January, 2021),
pp. 1549-1577, International Press of Boston
- Autry, EA; Carter, D; Herschlag, GJ; Hunter, Z; Mattingly, JC, METROPOLIZED MULTISCALE FOREST RECOMBINATION for REDISTRICTING,
Multiscale Modeling and Simulation, vol. 19 no. 4
(January, 2021),
pp. 1885-1914, Society for Industrial & Applied Mathematics (SIAM)
- Bakhtin, Y; Hurth, T; Lawley, SD; Mattingly, JC, Singularities of invariant densities for random switching between two linear ODEs in 2D,
SIAM Journal on Applied Dynamical Systems, vol. 20 no. 4
(January, 2021),
pp. 1917-1958
- Gao, Y; Kirkpatrick, K; Marzuola, J; Mattingly, J; Newhall, KA, LIMITING BEHAVIORS OF HIGH DIMENSIONAL STOCHASTIC SPIN ENSEMBLES*,
Communications in Mathematical Sciences, vol. 19 no. 2
(January, 2021),
pp. 453-494
- Gao, Y; Marzuola, JL; Mattingly, JC; Newhall, KA, Nonlocal stochastic-partial-differential-equation limits of spatially correlated noise-driven spin systems derived to sample a canonical distribution,
Physical Review E, vol. 102 no. 5
(November, 2020),
pp. 052112
- Leimbach, M; Mattingly, JC; Scheutzow, M, Noise-induced strong stabilization
(September, 2020)
- Herschlag, G; Mattingly, JC; Sachs, M; Wyse, E, Non-reversible Markov chain Monte Carlo for sampling of districting maps
(August, 2020)
- Autry, EA; Carter, D; Herschlag, G; Hunter, Z; Mattingly, JC, Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting
(August, 2020)
- Lu, Y; Mattingly, JC, Geometric ergodicity of Langevin dynamics with Coulomb interactions,
Nonlinearity, vol. 33 no. 2
(January, 2020),
pp. 675-699, IOP Publishing
- Carter, D; Hunter, Z; Teague, D; Herschlag, G; Mattingly, J, Optimal Legislative County Clustering in North Carolina,
Statistics and Public Policy, vol. 7 no. 1
(January, 2020),
pp. 19-29
- Herschlag, G; Kang, HS; Luo, J; Graves, CV; Bangia, S; Ravier, R; Mattingly, JC, Quantifying Gerrymandering in North Carolina,
Statistics and Public Policy, vol. 7 no. 1
(January, 2020),
pp. 30-38, Informa UK Limited
- Chikina, M; Frieze, A; Mattingly, JC; Pegden, W, Separating Effect From Significance in Markov Chain Tests,
Statistics and Public Policy, vol. 7 no. 1
(January, 2020),
pp. 101-114
- AGAZZI, A; MATTINGLY, JC, SEEMINGLY STABLE CHEMICAL KINETICS CAN BE STABLE, MARGINALLY STABLE, OR UNSTABLE,
Communications in Mathematical Sciences, vol. 18 no. 6
(January, 2020),
pp. 1605-1642, International Press of Boston
- Herzog, DP; Mattingly, JC, Ergodicity and Lyapunov Functions for Langevin Dynamics with Singular Potentials,
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, vol. 72 no. 10
(October, 2019),
pp. 2231-2255, WILEY
- Chin, A; Herschlag, G; Mattingly, J, The Signature of Gerrymandering in Rucho v. Common Cause,
South Carolina Law Review, vol. 70
(2019)
- Wang, C; Mattingly, J; Lu, YM, Scaling Limit: Exact and Tractable Analysis of Online Learning
Algorithms with Applications to Regularized Regression and PCA
(December, 2017)
- Johndrow, JE; Mattingly, JC, Error bounds for Approximations of Markov chains used in Bayesian
Sampling
(November, 2017)
- Herschlag, G; Ravier, R; Mattingly, JC, Evaluating Partisan Gerrymandering in Wisconsin
(September, 2017)
- Bakhtin, Y; Hurth, T; Lawley, SD; Mattingly, JC, Smooth invariant densities for random switching on the torus, vol. 31 no. 4
(August, 2017),
pp. 1331-1350, IOP Publishing
- Johndrow, JE; Mattingly, JC, Coupling and Decoupling to bound an approximating Markov Chain
(July, 2017)
- Glatt-Holtz, NE; Herzog, DP; Mattingly, JC, Scaling and Saturation in Infinite-Dimensional Control Problems with
Applications to Stochastic Partial Differential Equations,
Annals of PDE
(June, 2017)
- Bangia, S; Graves, CV; Herschlag, G; Kang, HS; Luo, J; Mattingly, JC; Ravier, R, Redistricting: Drawing the Line
(April, 2017)
- with Cooke, B; Herzog, DP; Mattingly, JC; Mckinle, SA; Schmidler, SC, Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential,
Communications in Mathematical Sciences, vol. 15 no. 7
(January, 2017),
pp. 1987-2025, International Press of Boston
- Hairer, M; Mattingly, J, The strong Feller property for singular stochastic PDEs, vol. 54 no. 3
(2016),
pp. 1314-1340, Institute of Mathematical Statistics
- Tempkin, JOB; Koten, BV; Mattingly, JC; Dinner, AR; Weare, J, Trajectory stratification of stochastic dynamics,
SIAM Review, vol. 60 no. 4
(2016),
pp. 909-938, Society for Industrial and Applied Mathematics
- Johndrow, JE; Mattingly, JC; Mukherjee, S; Dunson, D, Optimal approximating Markov chains for Bayesian inference
(August, 2015)
- Munch, E; Turner, K; Bendich, P; Mukherjee, S; Mattingly, J; Harer, J, Probabilistic Fréchet means for time varying persistence diagrams,
Electronic Journal of Statistics, vol. 9 no. 1
(January, 2015),
pp. 1173-1204, Institute of Mathematical Statistics
- Huckemann, S; Mattingly, JC; Miller, E; Nolen, J, Sticky central limit theorems at isolated hyperbolic planar singularities,
Electronic Journal of Probability, vol. 20
(2015),
pp. 1-34, Institute of Mathematical Statistics
- Glatt-Holtz, N; Richards, G; Mattingly, JC, On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations, vol. 166 no. 3-4
(2015),
pp. 618-649, Springer Nature
- Luo, S; Mattingly, JC, Scaling limits of a model for selection at two scales
(2015)
- Herzog, DP; Mattingly, JC, Noise-Induced Stabilization of Planar Flows II
(April, 2014)
- with Lawley, SD; Mattingly, JC; Reed, MC, Sensitivity to switching rates in stochastically switched ODEs,
Communications in Mathematical Sciences, vol. 12 no. 7
(2014),
pp. 1343-1352, International Press of Boston, ISSN 1539-6746
- Mattingly, JC; Pardoux, E, Invariant measure selection by noise. An example,
Discrete and Continuous Dynamical Systems. Series A, vol. 34 no. 10
(2014),
pp. 4223-4257, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947
- with Bakhtin, Y; Hurth, T; Mattingly, JC, Regularity of invariant densities for 1D-systems with random switching,
arXiv preprint arXiv:1406.5425, vol. 28 no. 11
(2014),
pp. 3755-3787, IOP Publishing, ISSN 0951-7715
- Lawley, SD; Mattingly, JC; Reed, MC, Stochastic switching in infinite dimensions with applications to random parabolic PDEs,
arXiv preprint arXiv:1407.2264, vol. 47 no. 4
(2014),
pp. 3035-3063, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
- Herzog, DP; Mattingly, JC, A practical criterion for positivity of transition densities,
arXiv preprint arXiv:1407.3858, vol. 28 no. 8
(2014),
pp. 2823-2845, IOP Publishing, ISSN 0951-7715
- Herzog, DP; Mattingly, JC, Noise-Induced Stabilization of Planar Flows I,
arXiv preprint arXiv:1404.0957, vol. 20
(2014), Institute of Mathematical Statistics
- with Mattingly, JC; Vaughn, C, Redistricting and the Will of the People,
arXiv preprint arXiv:1410.8796
(2014)
- 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, vol. 23 no. 6
(2013),
pp. 2238-2258, Institute of Mathematical Statistics, ISSN 1050-5164
- with Mattingly, JC; McKinley, SA; Pillai, NS, Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing,
Stochastic Processes and their Applications, vol. 122 no. 12
(December, 2012),
pp. 3953-3979, Elsevier BV, ISSN 0304-4149
- Luo, S; Reed, M; Mattingly, JC; Koelle, K, The impact of host immune status on the within-host and population dynamics of antigenic immune escape.,
J R Soc Interface, vol. 9 no. 75
(October, 2012),
pp. 2603-2613, The Royal Society
- with Athreyaz, A; Kolba, T; Mattingly, JC, Propagating lyapunov functions to prove noise-induced stabilization,
Electronic Journal of Probability, vol. 17
(2012),
pp. 1-38, Institute of Mathematical Statistics, ISSN 1083-6489
- Porporato, A; Kramer, PR; Cassiani, M; Daly, E; Mattingly, J, Local kinetic interpretation of entropy production through reversed diffusion.,
Phys Rev E Stat Nonlin Soft Matter Phys, vol. 84 no. 4 Pt 1
(Fall, 2011),
pp. 041142
- Koelle, K; Ratmann, O; Rasmussen, DA; Pasour, V; Mattingly, J, A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses,
Proceedings of the Royal Society B: Biological Sciences, vol. 278 no. 1725
(2011),
pp. 3723-3730, ISSN 0962-8452
- 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, Springer Nature, ISSN 0178-8051
- with Anderson, DF; Mattingly, JC, A weak trapezoidal method for a class of stochastic differential equations,
Communications in Mathematical Sciences, vol. 9 no. 1
(2011),
pp. 301-318, International Press of Boston, ISSN 1539-6746
- 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, Institute of Mathematical Statistics, ISSN 1083-6489
- Hairer, M; Mattingly, JC, Yet another look at Harris’ ergodic theorem for Markov chains,
in Progress in Probability, vol. 63
(2011),
pp. 109-117, Birkhäuser/Springer Basel AG, Basel
- with Heymann, M; Teitsworth, SW; Mattingly, JC, Rare Transition Events in Nonequilibrium Systems with State-Dependent
Noise: Application to Stochastic Current Switching in Semiconductor
Superlattices
(August, 2010)
- with Mattingly, JC; Pillai, NS; Stuart, AM, Diffusion limits of the random walk Metropolis algorithm in high
dimensions,
Annals of Applied Probability, vol. 22 no. 3
(March, 2010),
pp. 881-930, Institute of Mathematical Statistics
- 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, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
- Hairer, M; Mattingly, JC, Slow energy dissipation in anharmonic oscillator chains,
Communications on Pure and Applied Mathematics, vol. 62 no. 8
(2009),
pp. 999-1032, WILEY, ISSN 0010-3640
- with Hairer, M; Mattingly, JC, Spectral gaps in wasserstein distances and the 2d stochastic navier-stokes equations,
Annals of Probability, vol. 36 no. 6
(November, 2008),
pp. 2050-2091, Institute of Mathematical Statistics
- with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains
(August, 2008)
- Mattingly, JC; Suidan, TM, Transition measures for the stochastic Burgers equation,
in Integrable systems and random matrices, Contemp. Math., vol. 458
(2008),
pp. 409-418, Amer. Math. Soc., Providence, RI, Providence, RI, ISSN 0271-4132, ISBN 9780821842409
- with Iyer, G; Mattingly, J, A stochastic-Lagrangian particle system for the Navier-Stokes equations,
Nonlinearity, vol. 21 no. 11
(2008),
pp. 2537-2553, IOP Publishing, ISSN 0951-7715
- Anderson, DF; Mattingly, JC, Propagation of fluctuations in biochemical systems, II: Nonlinear chains.,
IET systems biology, vol. 1 no. 6
(November, 2007),
pp. 313-325, Institution of Engineering and Technology (IET), ISSN 1751-8849
- Mattingly, JC; Suidan, T; Vanden-Eijnden, E, Simple systems with anomalous dissipation and energy cascade,
Communications in Mathematical Physics, vol. 276 no. 1
(November, 2007),
pp. 189-220, Springer Nature, ISSN 0010-3616
- Bakhtin, Y; Mattingly, JC, Malliavin calculus for infinite-dimensional systems with additive noise,
Journal of Functional Analysis, vol. 249 no. 2
(August, 2007),
pp. 307-353, Elsevier BV, ISSN 0022-1236
- Anderson, DF; Mattingly, JC; Nijhout, HF; Reed, MC, Propagation of fluctuations in biochemical systems, I: linear SSC networks.,
Bulletin of mathematical biology, vol. 69 no. 6
(August, 2007),
pp. 1791-1813, Springer Nature, ISSN 0092-8240
- Lamba, H; Mattingly, JC; Stuart, AM, An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability,
IMA Journal of Numerical Analysis, vol. 27 no. 3
(January, 2007),
pp. 479-506, Oxford University Press (OUP), ISSN 0272-4979
- Mattingly, JC; Suidan, TM; Vanden-Eijnden, E, Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators,
Journal of Statistical Physics, vol. 128 no. 5
(2007),
pp. 1145-1152, Springer Nature, ISSN 0022-4715
- Nijhout, HF; Reed, MC; Anderson, DF; Mattingly, JC; James, SJ; Ulrich, CM, Erratum to H. Frederik Nijhout, et al. Epigenetics Volume 1, Issue 2; pp. 81-87.,
Epigenetics, vol. 1 no. 3
(July, 2006),
pp. 115-115, Informa UK Limited, ISSN 1559-2294
- Mattingly, JC; Pardoux, É, Malliavin calculus for the stochastic 2D Navier-Stokes equation,
Communications on Pure and Applied Mathematics, vol. 59 no. 12
(2006),
pp. 1742-1790, WILEY, ISSN 0010-3640
- Hairer, M; Mattingly, JC, Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing,
Annals of Mathematics, vol. 164 no. 3
(2006),
pp. 993-1032, Annals of Mathematics, Princeton U, ISSN 0003-486X
- Bakhtin, Y; Mattingly, JC, Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations,
Communications in Contemporary Mathematics, vol. 7 no. 5
(October, 2005),
pp. 553-582, World Scientific Pub Co Pte Lt, ISSN 0219-1997 (ISSN: 0219-1997.)
- Mattingly, JC; Suidan, TM, The small scales of the stochastic Navier-Stokes equations under rough forcing,
Journal of Statistical Physics, vol. 118 no. 1-2
(January, 2005),
pp. 343-364, Springer Nature, ISSN 0022-4715 (ISSN: 0022-4715.)
- Hairer, M; Mattingly, JC, Ergodic properties of highly degenerate 2D stochastic Navier-Stokes equations,
Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 339 no. 12
(2004),
pp. 879-882, Elsevier BV, ISSN 1631-073X (ISSN: 1631-073X.)
- Hairer, M; Mattingly, JC; Pardoux, É, Malliavin calculus for highly degenerate 2D stochastic Navier-Stokes equations,
Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 339 no. 11
(2004),
pp. 793-796, Elsevier BV, ISSN 1631-073X
- Hairer, M; Mattingly, JC; Pardoux, E, Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier–Stokes equation,
arXiv preprint math/0409057
(2004)
- Mattingly, JC, On recent progress for the stochastic Navier Stokes equations, vol. XV
(Summer, 2003),
pp. Exp. No. XI-52, Univ. 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}.)
- 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
- Mattingly, JC; Stuart, AM, Geometric ergodicity of some hypo-elliptic diffusions for particle motions,
Markov Processes and Related Fields, vol. 8 no. 2
(2002),
pp. 199-214, ISSN 1024-2953 (Inhomogeneous random systems (Cergy-Pontoise,
2001).)
- Mattingly, JC, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics,
Communications in Mathematical Physics, vol. 230 no. 3
(2002),
pp. 421-462, ISSN 0010-3616
- Mattingly, JC, Contractivity and ergodicity of the random map $x\mapsto\vert x-θ\vert $,
Rossi\u\i skaya Akademiya Nauk. Teoriya Veroyatnoste\u\i i ee Primeneniya, vol. 47 no. 2
(2002),
pp. 388-397, Society for Industrial & Applied Mathematics (SIAM), ISSN 0040-585X
- 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
(2002),
pp. 185-232, Elsevier BV, ISSN 0304-4149
- Mattingly, JC, The dissipative scale of the stochastics Navier-Stokes equation: regularization and analyticity,
Journal of Statistical Physics, vol. 108 no. 5-6
(2002),
pp. 1157-1179, ISSN 0022-4715 (Dedicated to David Ruelle and Yasha Sinai on
the occasion of their 65th birthdays.)
- Mattingly, JC, Contractivity and ergodicity of the random map $x\mapsto|x-\theta|$,
Teoriya Veroyatnostei i ee Primeneniya, vol. 47 no. 2
(2002),
pp. 388-397, Steklov Mathematical Institute
- E, W; Mattingly, JC, Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation,
Communications on Pure and Applied Mathematics, vol. 54 no. 11
(2001),
pp. 1386-1402, WILEY, ISSN 0010-3640
- 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
(2001),
pp. 83-106, ISSN 0010-3616 (Dedicated to Joel L. Lebowitz.)
- Holmes, PJ; Mattingly, JC; Wittenberg, RW, Low-Dimensional Models of Turbulence
(2001),
pp. 177-215, Springer Netherlands, ISBN 9780792369769
- Mattingly, JC, Ergodicity of $2$D Navier-Stokes equations with random forcing and large viscosity,
Communications in Mathematical Physics, vol. 206 no. 2
(1999),
pp. 273-288, Springer Nature, ISSN 0010-3616
- Mattingly, JC; Sinai, YG, An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations,
Communications in Contemporary Mathematics, vol. 1 no. 4
(1999),
pp. 497-516, World Scientific Pub Co Pte Lt
- Holmes, PJ; Lumley, JL; Berkooz, G; Mattingly, JC; Wittenberg, RW, Low-dimensional models of coherent structures in turbulence,
Physics Report, vol. 287 no. 4
(January, 1997),
pp. 337-384, Elsevier BV, ISSN 0370-1573
- 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
- Jonathan C. Mattingly, The Stochastic Navier-Stokes Equation: Energy Estimates and Phase Space Contraction,
PhD Thesis, Princeton University 1998
Papers Submitted
- with Stephan Huckemann, Ezra Miller, James Nolen, Sticky central limit theorems at isolated hyperbolic planar singularities
(October, 2014)
- with David P. Herzog, Noise-Induced Stabilization of Planar Flows II
(April, 2014)
- with David P. Herzog, Noise-Induced Stabilization of Planar Flows I
(April, 2014)
- with Sean D. Lawley and Michael C. Reed, Stochastic switching in infinite dimensions with applications to random parabolic PDEs
(2014)
- Elizabeth Munch, Paul Bendich, Katharine Turner, Sayan Mukherjee, Jonathan Mattingly, John Harer, Probabilistic Fréchet Means and Statistics on Vineyards
(2013)
Preprints
- 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)