# Jonathan Christopher Mattingly

- James B. Duke Distinguished Professor
- Professor of Mathematics

### Research Areas and Keywords

##### Analysis

Stochastic Analysis, Malliavin Calculus, Ergodic Theory

##### Biological Modeling

Stochastic and Random PDEs, Stochastic Dynamical Systems, Mathematical Ecology and Evolution, Metabolic and Cellular modeling, Out of equilibrium statistical mechanics

##### Computational Mathematics

Markov Chain Mixing, Stochastic Numerical Methods, High Dimensional Random Algorithms

##### PDE & Dynamical Systems

Stochastic and Random PDEs, Stochastic Dynamical Systems, Malliavin Calculus, Fluid Mechanics, Approximating invariant measures

##### Physical Modeling

Stochastic and Random PDEs, Stochastic Dynamical Systems, Fluid Mechanics

##### Probability

Stochastic and Random PDEs, Stochastic Dynamical Systems, Stochastic Analysis, Malliavin Calculus, Markov Chain Mixing, Ergodic Theory, High Dimensional Random Algorithms, Probability on stratified spaces, Out of equilibrium statistical mechanics, Approximating invariant measures

Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a Professor of Mathematics and of Statistical Science.

His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.

He is the recipient of a Sloan Fellowship and a PECASE CAREER award. He is also a fellow of the IMS and the AMS.

Mattingly, J. C. “Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity.” *Communications in Mathematical Physics*, vol. 206, no. 2, Jan. 1999, pp. 273–88. *Scopus*, doi:10.1007/s002200050706.
Full Text

Mattingly, J. C., and Y. G. Sinai. “An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations.” *Communications in Contemporary Mathematics*, vol. 1, no. 4, Jan. 1999, pp. 497–516. *Scopus*, doi:10.1142/S0219199799000183.
Full Text Open Access Copy

Holmes, P. J., et al. “Low-dimensional models of coherent structures in turbulence.” *Physics Report*, vol. 287, no. 4, Jan. 1997, pp. 337–84. *Scopus*, doi:10.1016/S0370-1573(97)00017-3.
Full Text

Mattingly, Jonathan C., et al. “Diffusion limits of the random walk Metropolis algorithm in high
dimensions.” *Annals of Applied Probability*, vol. 22, no. 3, pp. 881–930. *Arxiv*, doi:10.1214/10-AAP754.
Full Text Open Access Copy

Heymann, Matthias, et al. *Rare Transition Events in Nonequilibrium Systems with State-Dependent
Noise: Application to Stochastic Current Switching in Semiconductor
Superlattices*.
Open Access Copy

Chikina, Maria, et al. *Separating effect from significance in Markov chain tests*.
Open Access Copy

Carter, Daniel, et al. *A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling
of Redistricting Plans*.
Open Access Copy

Johndrow, James E., et al. *Optimal approximating Markov chains for Bayesian inference*.
Open Access Copy

Gao, Yuan, et al. *Non-local SPDE limits of spatially-correlated-noise driven spin systems
derived to sample a canonical distribution*.
Open Access Copy

Bangia, Sachet, et al. *Redistricting: Drawing the Line*.
Open Access Copy