Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems
type: Item
instance of: scholarly article
title: Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems
zbMATH Open document ID: 1022.60087
DOI: 10.1016/S0246-0203(02)01108-1
author: G. Panizo
author: C. Landim
author: Horng-Tzer Yau
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2003-03-11T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77731
review text: For a system of unbounded spins over the \(d\)-dimensional cube \(\{1,\ldots,L\}^d\), \(L\geq 1\), the paper considers evolutions governed by reversible conservative Ginzburg-Landau processes having Gaussian potential perturbed additively by bounded smooth functions \(F:\mathbb{R}\rightarrow\mathbb{R}\) with bounded derivative. The upper bounds of the form \(cL^2\), \(c\) being a constant depending on \(F\) and independent of \(d\), are established for the inverses of the spectral gap of the generators and of the constants in logarithmic Sobolev inequalities related to the processes (in the latter case \(||F''||_{\infty}<\infty\) is required). Following the approach developed by \textit{S. L. Lu} and \textit{H. T. Yau} [Commun. Math. Phys. 156, 399-433 (1993; Zbl 0779.60078)], the authors overcome the technical difficulties due to unboundedness of spins. The main ingredients of the proof are a local CLT uniform over the parameter and some sharp large deviations estimates.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1879933
zbMATH Keywords: diffusion process
zbMATH Keywords: Dirichlet form
zbMATH Keywords: spectral gap of generator
zbMATH Keywords: logarithmic Sobolev inequalities
zbMATH Keywords: spin system
zbMATH Keywords: Glauber dynamics
zbMATH Keywords: local central limit theorem
zbMATH Keywords: large deviations
reviewed by: Alexander V. Bulinski
MaRDI profile type: Publication
OpenAlex ID: W1597300024
description: scientific article; zbMATH DE number 1879933