https://hal.inria.fr/hal-01194679Luczak, MalwinaMalwinaLuczakDepartment of Mathematics London School of Economics - LSE - London School of Economics and Political ScienceConcentration of measure and mixing for Markov chainsHAL CCSD2008Markov chainsconcentration of measurerapid mixing[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]Episciences Iam, CoordinationRoesler, Uwe2015-09-07 12:51:022017-05-10 17:41:042015-09-07 12:56:45enConference papershttps://hal.inria.fr/hal-01194679/document10.46298/dmtcs.3558application/pdf1We 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.