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We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field…

Probability · Mathematics 2013-09-19 Francois Bolley , Arnaud Guillin , Cedric Villani

We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise…

Classical Analysis and ODEs · Mathematics 2010-09-21 François Bolley

We study heterogeneously interacting diffusive particle systems with mean-field type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration…

Probability · Mathematics 2026-01-14 Erhan Bayraktar , Donghan Kim

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

Probability · Mathematics 2022-11-03 Zachary Bezemek , Konstantinos Spiliopoulos

This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…

Probability · Mathematics 2021-06-24 Sarath Yasodharan , Rajesh Sundaresan

We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large…

Probability · Mathematics 2019-04-25 Julien Reygner

A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework…

Probability · Mathematics 2024-10-10 Louis-Pierre Chaintron

The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…

Probability · Mathematics 2020-11-24 Shi Jin , Lei Li

We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…

Probability · Mathematics 2026-03-03 Angeliki Koutsimpela , Stefan Grosskinsky

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

Probability · Mathematics 2025-11-03 Nicolai Jurek Gerber , Franca Hoffmann , Urbain Vaes

We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…

Probability · Mathematics 2022-10-07 Erhan Bayraktar , Suman Chakraborty , Ruoyu Wu

We investigate Gibbs measures for diffusive particles interacting through a two-body mean field energy. By identifying a gradient structure for the conditional law, we derive sharp bounds on the size of chaos, providing a quantitative…

Probability · Mathematics 2025-10-29 Zhenjie Ren , Songbo Wang

In this paper, we consider a system of heterogeneously interacting quantum particles subject to indirect continuous measurement. The interaction is assumed to be of the mean-field type. We derive a new limiting quantum graphon system, prove…

Analysis of PDEs · Mathematics 2024-05-15 Sofiane Chalal , Nina H. Amini , Gaoyue Guo , Hamed Amini

We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…

Probability · Mathematics 2020-11-17 Carlo Orrieri

We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…

Probability · Mathematics 2022-04-19 Alexander Stolyar

The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen…

Probability · Mathematics 2017-03-08 Eric Luçon

The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…

Analysis of PDEs · Mathematics 2019-09-04 Li Chen , Esther S. Daus , Ansgar Jüngel

In this paper, we consider graphon particle systems with heterogeneous mean-field type interactions and the associated finite particle approximations. Under suitable growth (resp. convexity) assumptions, we obtain uniform-in-time…

Probability · Mathematics 2022-10-21 Erhan Bayraktar , Ruoyu Wu

Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…

Probability · Mathematics 2021-01-01 Amarjit Budhiraja , Michael Conroy

This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…

Probability · Mathematics 2025-10-07 Louis-Pierre Chaintron , Antoine Diez
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