Relative entropy, Gaussian concentration and uniqueness of equilibrium states
Probability
2022-11-09 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2112.11326,
title = {Relative entropy, Gaussian concentration and uniqueness of equilibrium states},
author = {J. -R. Chazottes and F. Redig},
journal= {arXiv preprint arXiv:2112.11326},
year = {2022}
}
Comments
13 pages. Submitted