Large deviations and variational principle for harmonic crystals
type: Item
instance of: scholarly article
title: Large deviations and variational principle for harmonic crystals
zbMATH Open document ID: 0954.60091
DOI: 10.1007/PL00020962
published in: Communications in Mathematical Physics
publication date: 2001-01-25T00:00:00Z
review text: Author' summary: We consider massless Gaussian fields with covariance related to the Green function of a long range random walk on \({\mathbb{Z}}^d\). These are viewed as Gibbs measures for a linear-quadratic interaction. We establish thermodynamic identities and prove a version of Gibbs' variational principle, showing that translation invariant Gibbs measures are characterized as minimizers of the relative entropy density. We then study the large deviations of the empirical field of a Gibbs measure. We show that a weak large deviation principle holds at the volume order, with rate given by the relative entropy density.
reviewed by: Ostap Hryniv
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1422933
zbMATH Keywords: harmonic crystal
zbMATH Keywords: variational principle
zbMATH Keywords: large deviations
author: Pietro Caputo
author: Jean-Dominique Deuschel
MaRDI profile type: Publication
full work available at URL: pl00020962
OpenAlex ID: W1974520204
description: scientific article; zbMATH DE number 1422933