Relative entropy, Gaussian concentration and uniqueness of equilibrium states

Abstract

For a general class of lattice-spin systems, we prove that an abstract Gaussian concentration bound implies positivity of lower relative entropy density. As a consequence we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting. This extends earlier results from [Chazottes-Moles-REdig-Ugalde] with a different and very short proof.

13 pages. Submitted

References in corpus (3)

• On concentration inequalities and their applications for Gibbs measures in lattice systems
• Gaussian concentration and uniqueness of equilibrium states in lattice systems
• Dobrushin and Steif metrics are equal

Cited by in corpus (1)

• Dynamical Gibbs Variational Principles for Irreversible Interacting Particle Systems with Applications to Attractor Properties