1301.4146 (Tatiana Yarmola)

Sub-exponential mixing of random billiards driven by thermostats    [PDF]

Tatiana Yarmola

We study the class of open continuous-time mechanical particle systems introduced in the paper by Khanin and Yarmola \cite{Khanin}. Using the discrete-time results from \cite{Khanin} we demonstrate rigorously that, in continuous time, a unique steady state exists and is sub-exponentially mixing. Moreover, all initial distributions converge to the steady state and, for a large class of initial distributions, convergence to the steady state is sub-exponential. The main obstacle to exponential convergence is the existence of slow particles in the system.

View original: http://arxiv.org/abs/1301.4146