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Propagation of Chaos for 2D Log Gas on the Whole Space

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arxiv 2411.14777 v1 pith:XSFRPC74 submitted 2024-11-22 math.AP math.PR

Shuzhe Cai , Xuanrui Feng , Yun Gong , Zhenfu Wang This is my paper · ORCID
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keywords spacewholechaospropagationadaptingbjw23componentcoulomb
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We derive the quantitative propagation of chaos in the sense of relative entropy for the first time for the 2D Log gas or the weakly interacting particle systems with 2D Coulomb interactions on the whole space. We resolve this problem by adapting the modulated free energy method in [BJW23] to the whole space setting and establishing the crucial logarithmic growth estimates for the mean-field Poisson-Nernst-Planck (PNP) equation of single component via the parabolic maximum principle.

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Cited by 2 Pith papers

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  1. Sharp mean-field estimates for the repulsive log gas in any dimension

    math.PR 2025-06 conditional novelty 8.0 of 10

    The log-gas partition function is uniformly bounded in N for arbitrary bounded base measures, giving a mean-field convergence rate of order 1/N instead of (log N)/N for repulsive logarithmic interactions.

  2. Kac's Program for the Landau Equation

    math.AP 2025-06 conditional novelty 8.0 of 10

    The k-particle velocity marginals of Kac's particle system converge to the factorized law of the Landau solution for all power-law potentials, including Coulomb collisions, in weak, Wasserstein, entropic, and strong L...

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