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2011 Transportation-information inequalities for continuum Gibbs measures
Yutao Ma, Ran Wang, Liming Wu
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Electron. Commun. Probab. 16: 600-613 (2011). DOI: 10.1214/ECP.v16-1670

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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Yutao Ma. Ran Wang. Liming Wu. "Transportation-information inequalities for continuum Gibbs measures." Electron. Commun. Probab. 16 600 - 613, 2011. https://doi.org/10.1214/ECP.v16-1670

Information

Accepted: 10 October 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1254.60027
MathSciNet: MR2846653
Digital Object Identifier: 10.1214/ECP.v16-1670

Subjects:
Primary: 60E15. 60K35

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