Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing
Abstract
We consider a simple model for the fluctuating hydrodynamics of a flexible 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 fluid velocity field. This is a generalization of previous models which have used linear spring forces as well as white-in-time fluid 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. In addition we allow the possibility of excluding certain "bad" sets in phase space in which the assumptions are violated but from which the system leaves with a controllable probability. This allows for the treatment of singular drifts, such as those derived from the Lennard-Jones potential, which is a novel feature of this work.
Keywords
Cite
@article{arxiv.0902.4496,
title = {Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing},
author = {Jonathan C. Mattingly and Scott A. McKinley and Natesh S. Pillai},
journal= {arXiv preprint arXiv:0902.4496},
year = {2012}
}
Comments
A number of corrections and improvements. We thank the careful referee for useful suggestions and corrections