Hausdorff dimension of sets of generic points for Gibbs measures

B. M. Gurevich, A. A. Tempelman

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

For a translation invariant Gibbs measure v on the configuration space X of a lattice finite spin system, we consider the set Xμ of generic points. Using a Breiman type convergence theorem on the set X μ of generic points of an arbitrary translation invariant probability measure μ on X, we evaluate the Hausdorff dimension of the set Xμ with respect to any metric out of a wide class of "scale" metrics on X (including Billingsley metrics generated by Gibbs measures).

Original languageEnglish (US)
Pages (from-to)1281-1301
Number of pages21
JournalJournal of Statistical Physics
Volume108
Issue number5-6
DOIs
StatePublished - Dec 1 2002

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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