Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States

Journal article (2022)

Authors

Jean-René Chazottes Institut Polytechnique de Paris
F.H.J. Redig Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2022 Jean-René Chazottes, F.H.J. Redig
DOI: https://doi.org/10.3390/ e24111513
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the 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 with a different and very short proof.