Spatio-temporal large deviations principle for coupled circle maps.
type: Item
instance of: scholarly article
title: Spatio-temporal large deviations principle for coupled circle maps.
zbMATH Open document ID: 1054.60032
author: Jean-Baptiste Bardet
author: Gerard Ben Arous
published in: The Annals of Probability
publication date: 2004-09-15T00:00:00Z
review text: A large deviations principle (LDP) is established for the space-time empirical measure associated with certain dynamical systems, namely weakly coupled expanding circle maps on \(\mathbb{Z}^d\). To this end, the authors first construct a potential function \(\varphi\) defined on the state space \((S^1)^{\mathbb{Z}^d}\), and such that \((-\varphi)\) is playing the role of the logarithm of the Jacobian associated with the dynamics. This potential function appears naturally in a ``Volume lemma'' giving appropriate upper and lower bounds for the measure of all points whose orbit remains close to a fixed orbit; such bounds lie at the heart of the present work, and the announced LDP may then be established using thermodynamic formalism. Fortunately, many definitions and results concerning e.g. thermodynamic formalism are presented at the end of the article, which, altogether, is written with a very clear style.
reviewed by: Michel Sortais
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 37C35
Mathematics Subject Classification ID: 37C40
zbMATH DE Number: 2100731
zbMATH Keywords: coupled map lattices
zbMATH Keywords: large deviations
zbMATH Keywords: thermodynamic formalism
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1079021461
OpenAlex ID: W2057974727
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DOI: 10.1214/AOP/1079021461
description: scientific article; zbMATH DE number 2100731