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Preprints, Working Papers, ... Year : 2022

MEAN-FIELD LIMITS IN STATISTICAL DYNAMICS

François Golse
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Abstract

These lectures notes are aimed at introducing the reader to some recent mathematical tools and results for the mean-field limit in statistical dynamics. As a warm-up, lecture 1 reviews the approach to the mean-field limit in classical mechanics following the ideas of W. Braun, K. Hepp and R.L. Dobrushin, based on the notions of phase space empirical measures, Klimontovich solutions and Monge-Kantorovich-Wasserstein distances between probability measures. Lecture 2 discusses an analogue of the notion of Klimontovich solution in quantum dynamics, and explains how this notion appears in Pickl's method to handle the case of interaction potentials with a Coulomb type singularity at the origin. Finally, lecture 3 explains how the mean-field and the classical limits can be taken jointly on quantum N-particle dynamics, leading to the Vlasov equation. These lectures are based on a series of joint works with C. Mouhot and T. Paul.
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hal-03514290 , version 1 (06-01-2022)

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  • HAL Id : hal-03514290 , version 1

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François Golse. MEAN-FIELD LIMITS IN STATISTICAL DYNAMICS. 2022. ⟨hal-03514290⟩
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