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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


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.


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

Primary: 60E15. 60K35

Keywords: concentration inequality , Gibbs measure , Lyapunov function method , transportation-information inequality

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