Hypercontractivity and Gaussian isoperimetry. Applications to spin systems
type: Item
instance of: scholarly article
title: Hypercontractivity and Gaussian isoperimetry. Applications to spin systems
zbMATH Open document ID: 0983.60097
DOI: 10.1016/S0246-0203(00)00145-X
author: Pierre Fougères
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2002-04-21T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77675
review text: The author establishes a Gaussian isoperimetric inequality for a hypercontractive reversible diffusion generator on a compact Riemann manifold. The method of proof also allows to derive an isoperimetric inequality, weaker than that of S. Bobkov, for a hypercontractive reversible generator on a finite set. Applications are given to discrete spin systems of infinite range where exponential decay of correlations holds. For related work see \textit{E. Laroche} [Probab. Theory Relat. Fields 101, No. 1, 89-132 (1995; Zbl 0820.60082)].
reviewed by: Marius Iosifescu
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1552678
zbMATH Keywords: Gaussian isoperimetric inequality
zbMATH Keywords: hypercontractive reversible diffusion generator
zbMATH Keywords: discrete spin systems
MaRDI profile type: Publication
OpenAlex ID: W149830766
description: scientific article; zbMATH DE number 1552678