Ergodic theory of the symmetric inclusion process

TL;DR

This paper establishes a successful coupling for particles in the symmetric inclusion process, characterizes ergodic measures with finite moments, and provides conditions for convergence to invariant measures.

Contribution

It introduces a successful coupling approach for the symmetric inclusion process and characterizes ergodic measures with finite moments.

Findings

Successful coupling for n particles established

Characterization of ergodic measures with finite moments

Conditions for convergence to invariant measures derived

Abstract

We prove the existence of a successful coupling for $n$ particles in the symmetric inclusion process. As a consequence we characterize the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in the course of time to an invariant product measure.