The Annals of Probability

Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition

Liming Wu

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Abstract

In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincaré inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of the Liggett’s Mɛ theorem for interacting particle systems.

Article information

Source
Ann. Probab. Volume 34, Number 5 (2006), 1960-1989.

Dates
First available in Project Euclid: 14 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1163517230

Digital Object Identifier
doi:10.1214/009117906000000368

Mathematical Reviews number (MathSciNet)
MR2271488

Zentralblatt MATH identifier
1111.60079

Subjects
Primary: 60E15: Inequalities; stochastic orderings 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60G60: Random fields

Keywords
Poincaré inequality transportation inequality Gibbs measure Dobrushin’s uniqueness condition

Citation

Wu, Liming. Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition. Ann. Probab. 34 (2006), no. 5, 1960--1989. doi:10.1214/009117906000000368. https://projecteuclid.org/euclid.aop/1163517230.


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