### Abstract

For a translation invariant Gibbs measure v on the configuration space X of a lattice finite spin system, we consider the set X_{μ} 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_{μ} with respect to any metric out of a wide class of "scale" metrics on X (including Billingsley metrics generated by Gibbs measures).

Original language | English (US) |
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Pages (from-to) | 1281-1301 |

Number of pages | 21 |

Journal | Journal of Statistical Physics |

Volume | 108 |

Issue number | 5-6 |

DOIs | |

State | Published - Dec 1 2002 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Gurevich, B. M., & Tempelman, A. A. (2002). Hausdorff dimension of sets of generic points for Gibbs measures.

*Journal of Statistical Physics*,*108*(5-6), 1281-1301. https://doi.org/10.1023/A:1019760018782