On the validity of the log-Sobolev inequality for symmetric Fleming-Viot operators.

DOI10.1214/aop/1019160256zbMath1044.60037OpenAlexW1506949526MaRDI QIDQ1872141

Wilhelm Stannat

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1019160256

zbMATH Keywords

logarithmic Sobolev inequalitieshypercontractivityFleming-Viot operators

Mathematics Subject Classification ID

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

Related Items (15)

The logarithmic Sobolev inequality for the Wasserstein diffusion ⋮ Functional Inequalities for the Wasserstein Dirichlet Form ⋮ Regularity properties of semigroups generated by some Fleming--Viot type operators ⋮ Nash inequality for diffusion processes associated with Dirichlet distributions ⋮ Functional inequalities for the two-parameter extension of the infinitely-many-neutral-alleles diffusion ⋮ Functional inequalities for weighted gamma distribution on the space of finite measures ⋮ Spectral properties for a class of continuous state branching processes with immigration. ⋮ Analyticity of a class of degenerate evolution equations on the canonical simplex of \(\mathbb R^d\) arising from Fleming-Viot processes ⋮ Measure-valued continuous curves and processes in total variation norm ⋮ Analytic semigroups and some degenerate evolution equations defined on domains with corners ⋮ Poincar\'e Inequality for Dirichlet Distributions and Infinite-Dimensional Generalizations ⋮ Transportation cost inequalities for Wasserstein diffusions ⋮ Spectral gap for measure-valued diffusion processes ⋮ On the Simpson index for the Wright–Fisher process with random selection and immigration ⋮ Super Poincaré inequality for a dynamic model of the two-parameter Dirichlet process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The transition function of a Fleming-Viot process
• Line-of-descent and genealogical processes, and their applications in population genetics models
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Equations différentielles provenant de la genetique des populations
• Uniform positivity improving property, Sobolev inequalities, and spectral gaps
• An analytic approach to the Fleming-Viot processes with interactive selection
• An Example in the Theory of Hypercontractive Semigroups
• Fleming–Viot Processes in Population Genetics

This page was built for publication: On the validity of the log-Sobolev inequality for symmetric Fleming-Viot operators.