The Annals of Probability

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

Liming Wu

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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.

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

First available in Project Euclid: 14 November 2006

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Zentralblatt MATH identifier

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

Poincaré inequality transportation inequality Gibbs measure Dobrushin’s uniqueness condition


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.

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