Large deviation for weak Gibbs measures and multifractal spectra
type: Item
instance of: scholarly article
title: Large deviation for weak Gibbs measures and multifractal spectra
zbMATH Open document ID: 0979.28003
DOI: 10.1088/0951-7715/14/2/312
author: Marc Kesseböhmer
published in: Nonlinearity
publication date: 2002-02-03T00:00:00Z
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1595395
zbMATH Keywords: medium varying function
zbMATH Keywords: weak Gibbs measure
zbMATH Keywords: the Helmholtz free energy
zbMATH Keywords: large deviations
zbMATH Keywords: multifractal spectrum
zbMATH Keywords: entropy function
zbMATH Keywords: \(g\)-measures
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1088/0951-7715/14/2/312
OpenAlex ID: W2021763495
review text: The author introduces the class \({\mathcal D}\) of ``medium varying functions'' and corresponding weak Gibbs measures defined on a symbolic shift space. For \(\varphi, \psi \in {\mathcal D}\), \(\psi > 0\) and a weak Gibbs measure \(\mu\) for the potential \(\beta(0)\psi\), he proves that the Helmholtz free energy \(H(t)\) of the stochastic process \((S_{n_R}\varphi, \mu)_{R> 0}\) can be expressed in terms of the topological pressure. The Legendre transform of the convex function \(H\) is called the entropy function. Large deviation estimates are derived using the entropy function. These results are further related to the results of \textit{E. Olivier} [Nonlinearity 12, No. 6, 1571-1585 (1999; Zbl 0955.37003)] on multifractal spectra of Gibbs and \(g\)-measures.
reviewed by: Y. Xiao
description: scientific article