奇异riesz型扩散流的全局实时平均场收敛性

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2021-08-23 DOI:10.1214/22-aap1833

M. Rosenzweig, S. Serfaty

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引用次数: 22

摘要

考虑了具有$-\log|x|$或$|x|^{-s}$奇异相互作用的粒子系统的平均场极限，在$00$下，收敛在时间上是全局的，这是第一个在$\mathbb{R}^d$上的奇异设置下保守流和梯度流都有效的结果。该证明依赖于对Carlen-Loss的一个论证的改编，以显示极限方程解的衰减率，并依赖于对arXiv:1508.03377, arXiv:1803.08345, arXiv:2107.02592中提出的调制能量方法的改进，使得调制能量的时间导数中的所有前因子都由极限解的衰减界控制。

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Global-in-time mean-field convergence for singular Riesz-type diffusive flows

We consider the mean-field limit of systems of particles with singular interactions of the type $-\log|x|$ or $|x|^{-s}$, with $00$, the convergence is global in time, and it is the first such result valid for both conservative and gradient flows in a singular setting on $\mathbb{R}^d$. The proof relies on an adaptation of an argument of Carlen-Loss to show a decay rate of the solution to the limiting equation, and on an improvement of the modulated-energy method developed in arXiv:1508.03377, arXiv:1803.08345, arXiv:2107.02592 making it so that all prefactors in the time derivative of the modulated energy are controlled by a decaying bound on the limiting solution.

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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.