Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing

Details Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing

2009-02-26

arxiv.org/abs/0902.4496v2

Mathematics

Probability

A number of corrections and improvements. We thank the careful referee for useful suggestions and corrections

Scientific paper

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.

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