Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regime

弱相互作用温和解在随机偏微分方程中的混沌传播

Propagation of Chaos for Weakly Interacting Mild Solutions to Stochastic Partial Differential Equations

本文研究系数不满足Lipschitz条件的半线性随机偏微分方程弱相互作用温和解的混沌传播性质，并给出McKean-Vlasov随机偏微分方程温和解存在唯一性的连续性与线性增长条件。

分布于大型片段化种群中的性状演化：混沌传播与自适应动力学的结合

Evolution of a trait distributed over a large fragmented population: Propagation of chaos meets adaptive dynamics

本文研究大型片段化集合种群中的数量性状演化，通过混沌传播与自适应动力学建立空间Moran模型的积分微分及McKean–Vlasov极限，并导出含选择、漂变与迁移效应的新正则方程。

A propagation of chaos result for weakly interacting nonlinear Snell envelopes

In this article, we establish a propagation of chaos result for weakly interacting nonlinear Snell envelopes which converge to a class of mean-field reflected backward stochastic differential equations (BSDEs) with jumps and right-continuous and left-limited obstacle, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters both the driver and the lower obstacle. Under mild Lipschitz and integrability conditions on the coefficients, we prove existence and uniqueness of the solution to both the mean-field reflected BSDEs with jumps and the corres…

弱相互作用扩散的相变、对数Sobolev不等式及时间一致的混沌传播

Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions

本文研究了非凸势下弱相互作用扩散的平均场极限，探讨了LSI常数与相变关系，并证明LSI非退化性对时间一致的混沌传播和平衡涨落有重要影响。推广了无界自旋系统结果。

The enhanced Sanov theorem and propagation of chaos

We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the ($k$-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in rough path spaces and allows for a robust subsequent analysis of the particle system and its McKean-Vlasov type limit, as shown in two corollaries.

An Elementary Approach To Uniform In Time Propagation Of Chaos

Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of reflection and synchronous couplings applied to the individual particles. It provides explicit quantitative bounds that significantly extend previous results for the convex case.