Slow decay of Gibbs measures with heavy tails

Abstract

We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails in the case when spins are unbounded. The interactions are bounded and of finite range. The self-potential enters into two classes of measures, κ-concave probability measures and sub-exponential laws, for which it is known that no exponential decay can occur. Using coercive inequalities we prove that, for κ-concave probability measures, the associated infinite volume semi-group decays to equilibrium polynomially and stretched exponentially for sub-exponential laws. This improves and extends previous results by Bobkov and Zegarlinski. © 2009 Springer-Verlag.