Long-time behaviour and propagation of chaos for mean field kinetic particles

DOI10.1016/j.spa.2016.10.003zbMath1367.60121arXiv1603.03179OpenAlexW2536316288MaRDI QIDQ2359700

Pierre Monmarché

Publication date: 22 June 2017

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.03179

zbMATH Keywords

propagation of chaoshypocoercivitymean field interactionVlasov-Fokker-Planck equationkinetic particles

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Semilinear parabolic equations (35K58) Vlasov equations (35Q83) Fokker-Planck equations (35Q84)

Related Items (13)

Small mass limit in mean field theory for stochastic N particle system ⋮ Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes ⋮ Coupled McKean–Vlasov diffusions: wellposedness, propagation of chaos and invariant measures ⋮ Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics ⋮ A note on Fisher information hypocoercive decay for the linear Boltzmann equation ⋮ A Regularized Dean--Kawasaki Model: Derivation and Analysis ⋮ High-dimensional MCMC with a standard splitting scheme for the underdamped Langevin diffusion ⋮ Mean Field Limits for Interacting Diffusions with Colored Noise: Phase Transitions and Spectral Numerical Methods ⋮ The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium ⋮ The kinetic Fokker-Planck equation with mean field interaction ⋮ From weakly interacting particles to a regularised Dean–Kawasaki model ⋮ 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sanov property, generalized I-projection and a conditional limit theorem
• Stability of the front under a Vlasov-Fokker-Planck dynamics
• Quantitative concentration inequalities for empirical measures on non-compact spaces
• Short and long time behavior of the Fokker-Planck equation in a confining potential and applications
• Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition
• Phi-entropy inequalities for diffusion semigroups
• Hypocoercivity for kinetic equations with linear relaxation terms
• Logarithmic Sobolev inequalities for some nonlinear PDE's.
• Spectral decompositions and \(\mathbb{L}^2\)-operator norms of toy hypocoercive semi-groups
• Uniform convergence to equilibrium for granular media
• Hypocoercivity
• Analysis and Geometry of Markov Diffusion Operators
• Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation

This page was built for publication: Long-time behaviour and propagation of chaos for mean field kinetic particles