Browsing by Author "0297691"
Now showing items 120 of 53

A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses.
Koelle, K; Mattingly, Jonathan Christopher; Pasour, Virginia B; Rasmussen, DA; Ratmann, O (Proc Biol Sci, 20111222)Antigenically variable RNA viruses are significant contributors to the burden of infectious disease worldwide. One reason for their ubiquity is their ability to escape herd immunity through rapid antigenic evolution and ... 
A practical criterion for positivity of transition densities
Herzog, David P; Mattingly, Jonathan Christopher (Nonlinearity, 20150710)© 2015 IOP Publishing Ltd & London Mathematical Society.We establish a simple criterion for locating points where the transition density of a degenerate diffusion is strictly positive. Throughout, we assume that the diffusion ... 
A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs
Hairer, M; Mattingly, Jonathan Christopher (Electronic Journal of Probability, 20110509)We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. ... 
A weak trapezoidal method for a class of stochastic differential equations
Anderson, DF; Mattingly, Jonathan Christopher (Communications in Mathematical Sciences, 20110301)We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations ... 
An elementary proof of the existence and uniqueness theorem for the NavierStokes equations
Mattingly, Jonathan Christopher; Sinai, YG (Communications in Contemporary Mathematics, 19991101) 
Approximations of Markov Chains and HighDimensional Bayesian Inference
Dunson, David B; Johndrow, James E; Mattingly, Jonathan Christopher; Mukherjee, Sayan (2015) 
Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations
Hairer, M; Mattingly, Jonathan Christopher; Scheutzow, M (Probability Theory and Related Fields, 20110301)There are many Markov chains on infinite dimensional spaces whose onestep transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal ... 
Contractivity and ergodicity of the random map $x\mapsto
Mattingly, Jonathan Christopher (Теория вероятностей и ее применения, 2002) 
Contractivity and ergodicity of the random map x →
Mattingly, Jonathan Christopher (Theory of Probability and its Applications, 20030626)The long time behavior of the random map xn → xn+1 = xnθn is studied under various assumptions on the distribution of the θn. One of the interesting features of this random dynamical system is that for a single fixed ... 
Convergence of numerical timeaveraging and stationary measures via Poisson equations
Mattingly, Jonathan Christopher; Stuart, AM; Tretyakov, MV (SIAM Journal on Numerical Analysis, 20100707)Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for timeaveraging estimators are obtained and then used to show that the stationary behavior of ... 
Convergence of numerical timeaveraging and stationary measures via Poisson equations
Mattingly, Jonathan Christopher; Stuart, AM; Tretyakov, MV (SIAM Journal on Numerical Analysis, 20100707)Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for timeaveraging estimators are obtained and then used to show that the stationary behavior of ... 
Coupling and Decoupling to bound an approximating Markov Chain
Johndrow, James E; Mattingly, Jonathan Christopher (20170727)This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple ... 
Diffusion limits of the random walk metropolis algorithm in high dimensions
Mattingly, Jonathan Christopher; Pillai, NS; Stuart, AM (Annals of Applied Probability, 20120601)Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore ... 
Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials
Herzog, David P; Mattingly, Jonathan Christopher (20171130)We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the wellknown LennardJones type, and show that the system converges to the unique invariant Gibbs measure ... 
Ergodicity for the navierstokes equation with degenerate random forcing: Finitedimensional approximation
Weinan, E; Mattingly, Jonathan Christopher (Communications on Pure and Applied Mathematics, 20011101)We study Galerkin truncations of the twodimensional NavierStokes equation under degenerate, largescale, stochastic forcing. We identify the minimal set of modes that has to be forced in order for the system to be ergodic. ... 
Error bounds for Approximations of Markov chains
Johndrow, James E; Mattingly, Jonathan Christopher (20171130)The first part of this article gives error bounds for approximations of Markov kernels under FosterLyapunov conditions. The basic idea is that when both the approximating kernel and the original kernel satisfy a FosterLyapunov ... 
Evaluating Partisan Gerrymandering in Wisconsin
Herschlag, Gregory Joseph; Ravier, Robert; Mattingly, Jonathan Christopher (20170907)We examine the extent of gerrymandering for the 2010 General Assembly district map of Wisconsin. We find that there is substantial variability in the election outcome depending on what maps are used. We also found robust ... 
Evaluating Partisan Gerrymandering in Wisconsin
Ravier, Robert; Mattingly, Jonathan Christopher; Herschlag, Gregory Joseph (20171212) 
Geometric ergodicity of a beadspring pair with stochastic Stokes forcing
Mattingly, Jonathan Christopher; McKinley, Scott A; Pillai, NS (Stochastic Processes and their Applications, 20121201)We consider a simple model for the fluctuating hydrodynamics of a flexible polymer in a dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring ... 
Geometric ergodicity of Langevin dynamics with Coulomb interactions
Mattingly, Jonathan; Lu, YulongThis paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and ...