## 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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