Long-Time Behaviors of Mean-Field Interacting Particle Systems Related to McKean-Vlasov Equations

被引：22

作者：

Liu, Wei ^{[1
,2
]}

Wu, Liming ^{[3
,4
]}

Zhang, Chaoen ^{[3
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

[2] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Hubei, Peoples R China

[3] Harbin Inst Technol, Inst Adv Study Math, 92 West Da Zhi St, Harbin, Peoples R China

[4] Univ Clermont Auvergne UCA, Lab Math Blaise Pascal, CNRS, UMR 6620, F-63000 Clermont Ferrand, France

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2021年 / 387卷 / 01期

关键词：

SELF-STABILIZING PROCESSES; GRANULAR MEDIA EQUATIONS; INEQUALITIES; PROPAGATION; CONVERGENCE; EQUILIBRIUM; CHAOS; RATES;

D O I：

10.1007/s00220-021-04198-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we investigate concentration inequalities, exponential convergence in the Wasserstein metric W-1, and uniform-in-time propagation of chaos for the mean-field weakly interacting particle system related to McKean-Vlasov equation. By means of the known approximate componentwise reflection coupling and with the help of some new cost function, we obtain explicit estimates for those three problems, avoiding the technical conditions in the known results. Our results apply to possiblymulti-well confinement potentials, and interaction potentialsW with bounded second mixed derivatives del W-2(xy) which are not too big, so that there is no phase transition. Several examples are provided to illustrate the results.

引用

页码：179 / 214

页数：36

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