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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) Zbl 0882.60065

Azéma, J. (ed.) et al., Séminaire de probabilités XXXI. Berlin: Springer. Lect. Notes Math. 1655, 136-167 (1997).
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.
For the entire collection see [Zbl 0864.00069].

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
47A50 Equations and inequalities involving linear operators, with vector unknowns
47N30 Applications of operator theory in probability theory and statistics
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