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Journal of Statistical Physics

, Volume 108, Issue 5–6, pp 1281–1301 | Cite as

Hausdorff Dimension of Sets of Generic Points for Gibbs Measures

  • B. M. Gurevich
  • A. A. Tempelman
Article

Abstract

For a translation invariant Gibbs measure ν on the configuration space X of a lattice finite spin system, we consider the set X ν 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 X ν with respect to any metric out of a wide class of “scale” metrics on X (including Billingsley metrics generated by Gibbs measures).

Hausdorff dimension Gibbs measures generic points 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • B. M. Gurevich
    • 1
  • A. A. Tempelman
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Departments of Mathematics and StatisticsPenn State UniversityUniversity Park

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