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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya // Archive

Funktsional. Anal. i Prilozhen., 2002 Volume 36, Issue 3, Pages 68–71 (Mi faa207)

This article is cited in 4 papers

Brief communications

Hausdorff Dimension of the Set of Generic Points for Gibbs Measures

B. M. Gurevicha, A. A. Tempel'manb

a M. V. Lomonosov Moscow State University
b Pennsylvania State University

Abstract: For a Gibbs measure on the configuration space of a finite spin lattice system, we find (in terms of entropy) the Hausdorff dimension of the set of generic points. Using this result, we evaluate the Hausdorff dimension of level sets for Birkhoff ergodic averages of some continuous functions on the configuration space.

Keywords: Hausdorff dimension, Gibbs measures, ergodic averages, entropy.

UDC: 517.938

Received: 07.08.2001

DOI: 10.4213/faa207


 English version:
Functional Analysis and Its Applications, 2002, 36:3, 225–227

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