Mean square relaxation times for evolution of random fields

Abstract

We consider the problem of relaxation times for Markov evolution of systems composed of a countable number of locally interacting particles, each one of which has a finite phase space. We give a theorem for comparison of mean square relaxation times of evolutions possessing the same ergodic stationary state. We give a reduction theorem for “attractive” evolutions. The results are applied to a generalization of the Glauber evolution of the one dimensional Ising chain.