Relative entropy, Gaussian concentration and uniqueness of equilibrium states
| Autor: | Jean-René Chazottes, Frank Redig |
|---|---|
| Přispěvatelé: | Delft Institute of Applied Mathematics (DIAM), Delft University of Technology (TU Delft) |
| Rok vydání: | 2021 |
| Předmět: |
relative entropy density
concentration inequality translation-invariant Gibbs measure Probability (math.PR) General Physics and Astronomy FOS: Physical sciences Mathematical Physics (math-ph) [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] lattice spin systems FOS: Mathematics Mathematics - Probability Mathematical Physics |
| Zdroj: | Entropy; Volume 24; Issue 11; Pages: 1513 Entropy: international and interdisciplinary journal of entropy and information studies, 24(11) |
| ISSN: | 1099-4300 |
| DOI: | 10.48550/arxiv.2112.11326 |
| Popis: | 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. Comment: 13 pages. Submitted |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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