TY - JOUR
T1 - Some universal estimates on convergence to equilibrium in reversible Markov chains
AU - Shkolnikov, Mykhaylo
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the L2 norms. The estimates in total variation norm are obtained using a novel identity relating the convergence to equilibrium of a reversible Markov chain to the increase in the entropy of its one-dimensional distributions. In addition, for chains reversible with respect to the uniform measure, we show how the global convergence to equilibrium can be controlled using the entropy accumulated by the chain.
AB - We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the L2 norms. The estimates in total variation norm are obtained using a novel identity relating the convergence to equilibrium of a reversible Markov chain to the increase in the entropy of its one-dimensional distributions. In addition, for chains reversible with respect to the uniform measure, we show how the global convergence to equilibrium can be controlled using the entropy accumulated by the chain.
KW - Convergence to equilibrium
KW - Entropy
KW - Reversible Markov chains
KW - Time of coupling
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U2 - 10.1214/EJP.v18-1749
DO - 10.1214/EJP.v18-1749
M3 - Article
AN - SCOPUS:84873281512
VL - 18
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
SN - 1083-6489
ER -