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We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…

Probability · Mathematics 2020-01-16 Eric Luçon , Wilhelm Stannat

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

Probability · Mathematics 2026-05-06 Solesne Bourguin , Konstantinos Spiliopoulos

We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be non-linear and path…

Probability · Mathematics 2022-03-03 Rangel Baldasso , Alan Pereira , Guilherme Reis

In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…

Probability · Mathematics 2022-12-06 Maxime Hauray , Etienne Pardoux , Yen V. Vuong

The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…

Probability · Mathematics 2025-09-01 Robert Alexander Crowell

In this paper we intend to present a unified treatment of a variety of singular interacting particle systems and their McKean-Vlasov limits. This unified approach is based on the use of the relative entropy on the path space in the spirit…

Analysis of PDEs · Mathematics 2024-12-11 Patrick Cattiaux

Consider a system of $n$ weakly interacting particles driven by independent Brownian motions. In many instances, it is well known that the empirical measure converges to the solution of a partial differential equation, usually called…

Probability · Mathematics 2020-07-28 Florian Bechtold , Fabio Coppini

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

Probability · Mathematics 2023-07-17 Zachary Bezemek , Konstantinos Spiliopoulos

The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the…

Statistical Mechanics · Physics 2021-03-25 Yi Liao , Xiao-Bo Gong

We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…

Probability · Mathematics 2026-05-14 Sayan Banerjee , Andrew Nguyen

A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…

Probability · Mathematics 2023-01-25 Kai Du , Yifan Jiang , Xiaochen Li

We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…

Probability · Mathematics 2021-01-12 Zhen-Qing Chen , Wai-Tong Louis Fan

We study parameter estimation for interacting particle systems (IPSs) consisting of $N$ weakly interacting multivariate hypoelliptic SDEs. We propose a locally Gaussian approximation of the transition dynamics, carefully designed to address…

Statistics Theory · Mathematics 2025-09-19 Yuga Iguchi , Alexandros Beskos , Grigorios A. Pavliotis

In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…

Probability · Mathematics 2020-07-02 Jasper Hoeksema , Thomas Holding , Mario Maurelli , Oliver Tse

We consider nonparametric statistical inference on a periodic interaction potential $W$ from noisy discrete space-time measurements of solutions $\rho=\rho_W$ of the nonlinear McKean-Vlasov equation, describing the probability density of…

Statistics Theory · Mathematics 2025-01-15 Richard Nickl , Grigorios A. Pavliotis , Kolyan Ray

We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow…

Analysis of PDEs · Mathematics 2021-08-09 Julien Barré , Cedric Bernardin , Raphaël Chétrite , Yash Chopra , Mauro Mariani

This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal…

Probability · Mathematics 2026-04-17 Daniel Lacker , Lane Chun Yeung , Fuzhong Zhou

We consider interacting systems particle driven by i.i.d. fractional Brownian motions, subject to irregular, possibly distributional, pairwise interactions. We show propagation of chaos and mean field convergence to the law of the…

Probability · Mathematics 2025-12-02 Lucio Galeati , Khoa Lê , Avi Mayorcas

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Probability · Mathematics 2025-06-09 Pascal Bianchi , Walid Hachem , Victor Priser

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…

Statistical Mechanics · Physics 2008-10-01 E. Agliari , M. Casartelli , A. Vezzani
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