Large deviations for short recurrence
type: Item
instance of: scholarly article
title: Large deviations for short recurrence
zbMATH Open document ID: 1148.60010
author: Miguel Abadi
author: Sandro Vaienti
published in: Discrete and Continuous Dynamical Systems
publication date: 2008-07-29T00:00:00Z
review text: For a \(\psi\)-mixing dynamical system consider the function \(\tau(C_{n})/n, n=1,2,\dots\), where \(\tau(C_{n})\) is the first return time of a cylinder \(C_{n}\) to itself. \textit{B. Saussol, S. Troubetzkoy} and \textit{S. Vaienti} [J. Stat. Phys. 106, No. 3--4, 623--634 (2002; Zbl 1138.37300)] proved that \(\lim_{n\rightarrow\infty}\tau(C_{n})/n\) exists and is constant a.e. if the \(C_{n}\) are chosen in a descending sequence of cylinders around a given point. The present authors prove upper and lower bounds for the corresponding large deviation function. Actually, under mild assumptions they compute the large deviation function directly. The free energy function of \(\tau(C_{n})/n\) is also computed. Several examples illustrate the results obtained.
reviewed by: Marius Iosifescu
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 37A50
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 5304863
zbMATH Keywords: mixing
zbMATH Keywords: recurrence
zbMATH Keywords: overlapping
zbMATH Keywords: rare event
zbMATH Keywords: short correlation
zbMATH Keywords: large deviations
MaRDI profile type: Publication
full work available at URL: dcds.2008.21.729
OpenAlex ID: W2068923229
DOI: 10.3934/DCDS.2008.21.729
description: scientific article; zbMATH DE number 5304863