Critical large deviations for Gaussian fields in the phase transition regime. I
type: Item
instance of: scholarly article
title: Critical large deviations for Gaussian fields in the phase transition regime. I
zbMATH Open document ID: 0801.60018
author: Erwin Bolthausen
author: Jean-Dominique Deuschel
published in: The Annals of Probability
publication date: 1994-11-20T00:00:00Z
review text: The authors analyze large deviations for the empirical distributions of \(Z^ d\)-indexed stationary Gaussian random fields with \(d \geq 3\). The fields are assumed to have the covariance structure given by the Green function of an irreducible transient random walk. The volume normalization \((n^ d)\) is shown to govern large deviations outside of the Gibbsian class, and the weak large deviation principle is established. Precise asymptotics with normalization \(n^{d-2}\) is obtained within the Gibbsian class. The rate function in this case is given by the Dirichlet form of the diffusion associated with the covariance operator. The authors also give a spins' profile description of the field and show that smooth profiles obey large deviations with normalization \(n^{d-2}\), whereas discontinuous profiles obey large deviations with normalization \(n^{d-1}\).
reviewed by: Włodek Bryc
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 528624
zbMATH Keywords: large deviations
zbMATH Keywords: empirical distributions
zbMATH Keywords: random walk
zbMATH Keywords: weak large deviation principle
zbMATH Keywords: Dirichlet form
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989003
OpenAlex ID: W1978860619
DOI: 10.1214/AOP/1176989003
description: scientific article; zbMATH DE number 528624