Ergodicity and propagation of chaos for mean field kinetic particles

2016/03/10 by Pierre Monmarché, Monmarché, Pierre
Mathematics · Physics and Astronomy · #35K58 #60J60 #82B40 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Probability (math.PR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1603.03179

openalex publication_date 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation in the presence of a convex external potential, without smallness restriction on the interaction. From this are derived uniform in time propagation of chaos estimates, which themselves yield in turn an exponentially fast convergence for the semi-linear equation itself. The approach is quantitative.

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