Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes

Abstract

Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation. Under some conditions (that allow non-convex confining potentials) the convergence rate is proven to be independent from the number of particles. From this are derived uniform in time propagation of chaos estimates and an exponentially fast convergence for the nonlinear equation itself.

References in corpus (1)

• The Kinetic Fokker-planck Equation With Mean Field Interaction

Cited by in corpus (10)

• Propagation of chaos: a review of models, methods and applications. II. Applications
• Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models
• Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics
• Propagation of chaos: a review of models, methods and applications. I. Models and methods
• Uniform-in-time propagation of chaos for mean field Langevin dynamics
• Uniform-in-time propagation of chaos for the Cucker--Smale model
• On the exponential ergodicity of the McKean-Vlasov SDE depending on a polynomial interaction
• An entropic approach for Hamiltonian Monte Carlo: the idealized case
• Self-interacting approximation to McKean-Vlasov long-time limit: a Markov chain Monte Carlo method
• Some remarks on the effect of the Random Batch Method on phase transition