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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

In the series of models with interacting particles in stochastic geometry, a new contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat…

Probability · Mathematics 2015-04-02 Jakub Vecera , Viktor Benes

We consider interacting particle dynamics with Vicsek type interactions, and their macroscopic PDE limit, in the non-mean-field regime; that is, we consider the case in which each particle/agent in the system interacts only with a…

Pattern Formation and Solitons · Physics 2022-06-15 P. Buttà , B. Goddard , T. M. Hodgson , M. Ottobre , K. J. Painter

This paper considers an $n$-particle jump-diffusion system with mean filed interaction, where the coefficients are locally Lipschitz continuous. We address the convergence as $n\to\infty$ of the empirical measure of the jump-diffusions to…

Probability · Mathematics 2024-02-27 Zeqian Li

Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…

Mathematical Physics · Physics 2021-03-17 Yu-Chen Cheng , Hong Qian

Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…

Dynamical Systems · Mathematics 2021-05-20 Denis D. Patterson , Simon A. Levin , A. Carla Staver , Jonathan D. Touboul

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

We study a stochastic individual-based model of interacting plant and pollinator species through a bipartite graph: each species is a node of the graph, an edge representing interactions between a pair of species. The dynamics of the system…

Probability · Mathematics 2025-08-27 Sylvain Billiard , Hélène Leman , Thomas Rey , Viet Chi Tran

We study a stochastic compartmental susceptible-infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval $[0,T],$ for some $ T>0$. In this setting, we split the…

Probability · Mathematics 2021-10-18 Wasiur R. KhudaBukhsh , Casper Woroszylo , Grzegorz A. Rempała , Heinz Koeppl

We prove a central limit theorem characterizing the small noise fluctuations of stochastic PDEs of fluctuating hydrodynamics type. The results apply to the case of nonlinear and potentially degenerate diffusions and irregular noise…

Probability · Mathematics 2023-11-01 Andrea Clini , Benjamin Fehrman

In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…

Probability · Mathematics 2024-12-19 Yuewen Hou , Yun Li , Longjie Xie

Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…

Probability · Mathematics 2025-01-07 Lei Li , Yuelin Wang , Yuliang Wang

Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with…

Probability · Mathematics 2018-02-05 Franco Flandoli , Enrico Priola , Giovanni Zanco

In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component…

Probability · Mathematics 2025-09-30 Jie Xiang , Huijie Qiao

We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…

Probability · Mathematics 2025-02-19 Eva Löcherbach , Dasha Loukianova , Elisa Marini

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

Probability · Mathematics 2021-06-09 Michael Röckner , Longjie Xie , Li Yang

We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics of the particles are formulated as measure-valued…

Probability · Mathematics 2025-01-22 Max Heldman , Samuel A. Isaacson , Qianhan Liu , Konstantinos Spiliopoulos

We establish a central limit theorem and large deviations principle that characterises small noise fluctuations of the generalised Dean--Kawasaki stochastic PDE. The fluctuations agree to first order with fluctuations of certain interacting…

Probability · Mathematics 2025-04-25 Shyam Popat

In this paper we consider an interacting particle system in $\mathbb{R}^d$ modelled as a system of $N$ stochastic differential equations driven by L\'evy processes. The limiting behaviour as the size $N$ grows to infinity is achieved as a…

Probability · Mathematics 2019-09-12 Christian Olivera , Marielle Simon

We examine the fluctuations of the empirical density measure for the colour version of the symmetric nearest neighbour zero range particle systems in dimension one. We show that the weak limit of these fluctuations is the solution of a…

Probability · Mathematics 2007-05-23 Hanna Jankowski
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