Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 16 (2011), paper no. 52, 600-613.
Transportation-information inequalities for continuum Gibbs measures
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.
Electron. Commun. Probab., Volume 16 (2011), paper no. 52, 600-613.
Accepted: 10 October 2011
First available in Project Euclid: 7 June 2016
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E15. 60K35
This work is licensed under aCreative Commons Attribution 3.0 License.
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