The Annals of Probability
- Ann. Probab.
- Volume 34, Number 5 (2006), 1960-1989.
Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition
Full-text: Open access
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 M−ɛ 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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