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Transportation-information inequalities for continuum Gibbs measures. (English) Zbl 1254.60027

Summary: 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.

MSC:

60E15 Inequalities; stochastic orderings
60K25 Queueing theory (aspects of probability theory)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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