Pith. sign in

REVIEW 3 cited by

Mean-Field Limits in Statistical Dynamics

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2201.02005 v1 pith:T6QLIOWZ submitted 2022-01-06 math-ph math.APmath.MP

Mean-Field Limits in Statistical Dynamics

Fran\c{c}ois Golse This is my paper
classification math-ph math.APmath.MP
keywords dynamicsmean-fieldlectureclassicalexplainsklimontovichlectureslimit
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original 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.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Singular mean-field limits via a multiscale mollification metric

    math.AP 2026-07 accept novelty 8.0

    Multiscale mollification by heat kernels yields quantitative mean-field limits for singular particle systems (sub-Coulomb global, Coulomb short-time in d≥3, super-Coulomb N-dependent), optimal by collision examples.

  2. Wasserstein gradient flows for Coulomb discrepancies

    math.AP 2026-07 accept novelty 7.0

    Under Coulomb MMD energy, the Wasserstein gradient flow converges exponentially to uniformly positive targets under PL-type coercivity, exhibits rigidity of critical points, and admits no uniform whole-space convergence rate.

  3. Wasserstein gradient flows for Coulomb discrepancies

    math.AP 2026-07 conditional novelty 6.5

    Wasserstein gradient flows of Coulomb MMD exist globally, become instantly bounded, decay exponentially on the torus via a defective PL inequality, but face spatial-infinity obstructions on R^d.