Hausdorff dimension of sets of generic points for Gibbs measures

B. M. Gurevich; A. A. Tempelman

doi:10.1023/A:1019760018782

Hausdorff dimension of sets of generic points for Gibbs measures

B. M. Gurevich, A. A. Tempelman

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8 Scopus citations

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)
Pages (from-to)	1281-1301
Number of pages	21
Journal	Journal of Statistical Physics
Volume	108
Issue number	5-6
DOIs	https://doi.org/10.1023/A:1019760018782
State	Published - 2002

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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author = "Gurevich, {B. M.} and Tempelman, {A. A.}",

note = "Funding Information: The authors are grateful to Marina Tempelman for varied assistance in preparation of this paper. This research was partially supported by RFBR, Grant 02-01-00444.",

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AU - Tempelman, A. A.

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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).

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -

Hausdorff dimension of sets of generic points for Gibbs measures

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