Uniform Poincaré and logarithmic Sobolev inequalities for mean field particle systems

DOI10.1214/21-AAP1707zbMath1503.60150arXiv1909.07051MaRDI QIDQ2170354

Wei Liu, Chaoen Zhang, Li-ming Wu, Arnaud Guillin

Publication date: 5 September 2022

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

Full work available at URL: https://arxiv.org/abs/1909.07051

zbMATH Keywords

logarithmic Sobolev inequalityPoincaré inequalityMcKean-Vlasov equationmean field particle models

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Applications of stochastic analysis (to PDEs, etc.) (60H30)

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Exponential ergodicity for singular reflecting McKean-Vlasov SDEs, Stationary solutions and local equations for interacting diffusions on regular trees, Uniqueness of stationary distribution and exponential convergence for distribution dependent SDEs, Asymptotic behaviors of small perturbation for multivalued Mckean-Vlasov stochastic differential equations, Wasserstein contraction and Poincaré inequalities for elliptic diffusions with high diffusivity, Exponential ergodicity for non-dissipative McKean-Vlasov SDEs, Distribution dependent stochastic differential equations, Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases, Propagation of chaos: a review of models, methods and applications. II: Applications

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