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Concentration of measure and mixing for Markov chains

Abstract : We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We illustrate our results with applications to some known chains from computer science and statistical mechanics.
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Malwina Luczak. Concentration of measure and mixing for Markov chains. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. pp.95-120. ⟨hal-01194679⟩

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