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Dimensions and Waiting Times for Gibbs Measures

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Abstract

For shifts of finite type, we relate the waiting time between two different orbits, one chosen according to an ergodic measure, the other according to a Gibbs measure, to Billingsley dimensions of generic sets. This is achieved by computing Billingsley dimensions of saturated sets in terms of a relative entropy which satisfies a pointwise ergodic result. As a by-product, a similar result is obtained for match lengths that are dual quantities of waiting times.

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Authors and Affiliations

  1. CPT-CNRS, Luminy Case 907, F-13288, Marseille Cedex 9, France

    Jean-René Chazottes

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  1. Jean-René Chazottes
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Chazottes, JR. Dimensions and Waiting Times for Gibbs Measures. Journal of Statistical Physics 98, 305–320 (2000). https://doi.org/10.1023/A:1018683024003

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  • DOI: https://doi.org/10.1023/A:1018683024003

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