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Zbl 0882.60065
Miclo, Laurent
Remarks on hypercontractivity and entropy evolution of finite Markov chains. (Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaînes de Markov finies.) (French)
[A] Azéma, J. (ed.) et al., Séminaire de probabilités XXXI. Berlin: Springer. Lect. Notes Math. 1655, 136-167 (1997). ISBN 3-540-62634-4/pbk

The author shows the usefulness of certain Sobolev logarithmic inequalities in studying hypercontractivity and evolution of entropy for finite-state discrete-time homogeneous Markov chains. An application is given to generalized simulated annealing algorithms in discrete time.
[M.Iosifescu (Bucureşti)]

MSC 2000:: *60J10 Markov chains with discrete parameter
47A50 Equations and inequalities involving linear operators
47N30 Appl. of operator theory in probability theory and statistics

Keywords: Sobolev logarithmic inequalities; hypercontractivity; simulated annealing algorithms

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