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On the validity of the log-Sobolev inequality for symmetric Fleming-Viot operators. (English) Zbl 1044.60037

Summary: We prove that Fleming-Viot operators with parent-independent mutation satisfy a logarithmic Sobolev inequality if and only if the set of types is finite.

MSC:

60G57 Random measures
35P15 Estimates of eigenvalues in context of PDEs
60K35 Interacting random processes; statistical mechanics type models; percolation theory
46N30 Applications of functional analysis in probability theory and statistics
60J35 Transition functions, generators and resolvents
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