Geometric ergodicity for dissipative particle dynamics

Dissipative particle dynamics is a model of multi-phase fluid flows described by a system of stochastic differential equations. We consider the problem of N particles evolving on the one-dimensional periodic domain of length L and, if the density of particles is large, prove geometric convergence to a unique invariant measure. The proof uses minorization and drift arguments, but allows elements of the drift and diffusion matrix to have compact support, in which case hypoellipticity arguments are not directly available. © 2006 World Scientific Publishing Company.