Transportation-information inequalities for continuum Gibbs measures

Yutao Ma (Beijing Normal University)
Ran Wang (Wuhan University)
Liming Wu (Chinese Academy of Sciences and Université Blaise Pascal)

Abstract


The objective of this paper is to establish explicit concentration inequalities for the Glauber dynamics related with continuum or discrete Gibbs measures. At first we establish the optimal transportation-information $W_1 I$-inequality for the $M/M/\infty$-queue associated with the Poisson measure, which improves several previous known results. Under the Dobrushin's uniqueness condition, we obtain some explicit $W_1 I$-inequalities for Gibbs measures both in the continuum and in the discrete lattice. Our method is a combination of Lipschitzian spectral gap, the Lyapunov test function approach and the tensorization technique.

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Pages: 600-613

Publication Date: October 10, 2011

DOI: 10.1214/ECP.v16-1670

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