Hausdorff dimension of sets of generic points for Gibbs measures

B. M. Gurevich, Arkady Tempelman

Research output: Contribution to journalArticle

8 Citations (Scopus)

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

Fingerprint

Gibbs Measure
Hausdorff Dimension
Invariant Measure
Metric
Spin Systems
Configuration Space
Convergence Theorem
Probability Measure
theorems
Evaluate
Arbitrary
configurations

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Gurevich, B. M. ; Tempelman, Arkady. / Hausdorff dimension of sets of generic points for Gibbs measures. In: Journal of Statistical Physics. 2002 ; Vol. 108, No. 5-6. pp. 1281-1301.
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Hausdorff dimension of sets of generic points for Gibbs measures. / Gurevich, B. M.; Tempelman, Arkady.

In: Journal of Statistical Physics, Vol. 108, No. 5-6, 01.12.2002, p. 1281-1301.

Research output: Contribution to journalArticle

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