Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States

Jean René Chazottes; Frank Redig

doi:10.3390/e24111513

Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States

Jean René Chazottes
, Frank Redig

Delft Institute of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	1513
Journal	Entropy
Volume	24
Issue number	11
DOIs	https://doi.org/10.3390/e24111513
Publication status	Published - 1 Nov 2022

Keywords

concentration inequality
lattice spin systems
relative entropy density
translation-invariant Gibbs measure

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title = "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 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.",

keywords = "concentration inequality, lattice spin systems, relative entropy density, translation-invariant Gibbs measure",

author = "Chazottes, \{Jean Ren{\'e}\} and Frank Redig",

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AU - Redig, Frank

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N2 - 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.

AB - 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.

KW - concentration inequality

KW - lattice spin systems

KW - relative entropy density

KW - translation-invariant Gibbs measure

U2 - 10.3390/e24111513

DO - 10.3390/e24111513

M3 - Article

AN - SCOPUS:85141724706

SN - 1099-4300

VL - 24

JO - Entropy

JF - Entropy

IS - 11

M1 - 1513

ER -

Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States

Abstract

Keywords

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