Electronic Communications in Probability

Transportation-information inequalities for continuum Gibbs measures

Yutao Ma, Ran Wang, and Liming Wu

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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.

Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 52, 600-613.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465262008

Digital Object Identifier
doi:10.1214/ECP.v16-1670

Mathematical Reviews number (MathSciNet)
MR2846653

Zentralblatt MATH identifier
1254.60027

Subjects
Primary: 60E15. 60K35

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Ma, Yutao; Wang, Ran; Wu, Liming. Transportation-information inequalities for continuum Gibbs measures. Electron. Commun. Probab. 16 (2011), paper no. 52, 600--613. doi:10.1214/ECP.v16-1670. https://projecteuclid.org/euclid.ecp/1465262008


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