### 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 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

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

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*Journal of Statistical Physics*, vol. 108, no. 5-6, pp. 1281-1301. https://doi.org/10.1023/A:1019760018782

**Hausdorff dimension of sets of generic points for Gibbs measures.** / Gurevich, B. M.; Tempelman, Arkady.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Hausdorff dimension of sets of generic points for Gibbs measures

AU - Gurevich, B. M.

AU - Tempelman, Arkady

PY - 2002/12/1

Y1 - 2002/12/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0141450312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141450312&partnerID=8YFLogxK

U2 - 10.1023/A:1019760018782

DO - 10.1023/A:1019760018782

M3 - Article

AN - SCOPUS:0141450312

VL - 108

SP - 1281

EP - 1301

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5-6

ER -