相关论文: Sharp uniform-in-time mean-field convergence for s…

We consider the mean-field limit of systems of particles with singular interactions of the type $-\log|x|$ or $|x|^{-s}$, with $0< s<d-2$, and with an additive noise in dimensions $d \geq 3$. We use a modulated-energy approach to prove a…

We provide a proof of mean-field convergence of first-order dissipative or conservative dynamics of particles with Riesz-type singular interaction (the model interaction is an inverse power $s$ of the distance for any $0<s<d$) when assuming…

This paper is concerned with the mean-field limit for the gradient flow evolution of particle systems with pairwise Riesz interactions, as the number of particles tends to infinity. Based on a modulated energy method, using regularity and…

We consider mean-field limits for overdamped Langevin dynamics of $N$ particles with possibly singular interactions. It has been shown that a modulated free energy method can be used to prove the mean-field convergence or propagation of…

We provide an estimation of the dissipation of the Wasserstein 2 distance between the law of some interacting $N$-particle system, and the $N$ times tensorized product of solution to the corresponding limit nonlinear conservation law. It…

We investigate the large time behavior of $N$ particles restricted to a smooth closed curve in $\mathbb{R}^d$ and subject to a gradient flow with respect to Euclidean hyper-singular repulsive Riesz $s$-energy with $s>1.$ We show that…

We prove functional inequalities in any dimension controlling the iterated derivatives along a transport of the Coulomb or super-Coulomb Riesz modulated energy in terms of the modulated energy itself. This modulated energy was introduced by…

We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary…

This note extends the modulated entropy and free energy methods for proving mean-field limits/propagation of chaos to the whole space without any confining potential, in contrast to previous work limited to the torus or requiring…

We prove a functional inequality in any dimension controlling the derivative along a transport of the Riesz modulated energy in terms of the modulated energy itself. This modulated energy was introduced by the third author and collaborators…

We study McKean--Vlasov Stochastic Differential Equations (MV-SDEs) whose drift and diffusion coefficients are of superlinear growth in \textit{all} their variables thus also superlinear in the measure component (the meaning is specified in…

Time-uniform log-Sobolev inequalities (LSI) satisfied by solutions of semi-linear mean-field equations have recently appeared to be a key tool to obtain time-uniform propagation of chaos estimates. This work addresses the more general…

Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distances for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long…

In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…

We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of…

We study the problem of convergence of the normalized Ricci flow evolving on a compact manifold $\Omega$ without boundary. In \cite{KS10, KS15} we derived, via PDE techniques, global-in-time existence of the classical solution and…

We study the quantitative convergence of Wasserstein gradient flows of Kernel Mean Discrepancy (KMD) (also known as Maximum Mean Discrepancy (MMD)) functionals. Our setting covers in particular the training dynamics of shallow neural…

In this paper, uniform in time quantitative propagation of chaos in $L^1$-Wasserstein distance for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting and the drift is assumed to…

We prove universality of a macroscopic behavior of solutions of a large class of semi-linear parabolic SPDEs on $\mathbb{R}_+\times\mathbb{T}$ with fractional Laplacian $(-\Delta)^{\sigma/2}$, additive noise and polynomial non-linearity,…

The theory of Wasserstein gradient flows in the space of probability measures has made an enormous progress over the last twenty years. It constitutes a unified and powerful framework in the study of dissipative partial differential…