Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition

DOI10.1214/009117906000000368zbMath1111.60079arXivmath/0611635OpenAlexW3102436459MaRDI QIDQ858988

Li-ming Wu

Publication date: 12 January 2007

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611635

zbMATH Keywords

Poincaré inequalitytransportation inequality

Mathematics Subject Classification ID

Random fields (60G60) Inequalities; stochastic orderings (60E15) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (13)

Exponential convergence of fisher entropy for diffusion processes ⋮ Characterization of a class of weak transport-entropy inequalities on the line ⋮ A spectral condition for spectral gap: fast mixing in high-temperature Ising models ⋮ Transport-information inequalities for Markov chains ⋮ Mixing and concentration by Ricci curvature ⋮ Transportation inequalities: from Poisson to Gibbs measures ⋮ Intertwining and commutation relations for birth-death processes ⋮ The Poincaré inequality for Markov random fields proved via disagreement percolation ⋮ Convergence rate and concentration inequalities for Gibbs sampling in high dimension ⋮ Comparison theorems for Gibbs measures ⋮ Spectral gap and logarithmic Sobolev constant for continuous spin systems ⋮ Convergence rates of symmetric scan Gibbs sampler ⋮ Coupling, concentration inequalities, and stochastic dynamics

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