University of Warwick. Centre for Research in Statistical Methodology
Abstract
We consider a simple model for the
uctuating hydrodynamics of a
exible polymer
in dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being advected by a
stochastic Stokes
uid velocity field. This is a generalization of previous models which
have used linear spring forces as well as white-in-time
uid velocity fields.
We follow previous work combining control theoretic arguments, Lyapunov functions, and hypo-elliptic diffusion theory to prove exponential convergence via a Harris
chain argument. To this, we add the possibility of excluding certain "bad" sets in phase
space in which the assumptions are violated but from which the systems leaves with a
controllable probability. This allows for the treatment of singular drifts, such as those
derived from the Lennard-Jones potential, which is an novel feature of this work