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Related papers: Rigorous mean-field limit and cross diffusion

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This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…

Probability · Mathematics 2023-07-21 Anirudh Sridhar , Soummya Kar

Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…

Analysis of PDEs · Mathematics 2025-07-30 Sebastian Throm

We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the…

Probability · Mathematics 2013-09-19 François Bolley

We study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system coupling leader particles with a follower fluid, and then to a…

Analysis of PDEs · Mathematics 2025-08-07 Giacomo Albi , Young-Pil Choi , Matteo Piu , Sihyun Song

We study a stochastic epidemic model consisting of elements (organisms in a community or cells in tissue) with fixed positions, in which damage or disease is transmitted by diffusing agents ("signals") emitted by infected individuals. The…

Populations and Evolution · Quantitative Biology 2015-06-05 Fernando P. Faria , Ronald Dickman

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

We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…

Probability · Mathematics 2021-07-19 Erhan Bayraktar , Ruoyu Wu

This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…

Probability · Mathematics 2025-11-21 Pierre-Emmanuel Jabin , David Poyato , Juan Soler

We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as…

Probability · Mathematics 2026-03-24 Nikolaos Kolliopoulos , Martin Larsson , Zeyu Zhang

A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…

Analysis of PDEs · Mathematics 2018-12-24 Ansgar Jüngel , Christian Kuehn , Lara Trussardi

A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…

Adaptation and Self-Organizing Systems · Physics 2009-10-31 Alan McKane , David Alonso , Ricard V. Sole

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

Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…

Probability · Mathematics 2026-05-20 Eliana Fausti , Andreas Sojmark

A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a three-dimensional variational…

Mathematical Physics · Physics 2018-04-04 Diego Alberici , Emanuele Mingione

We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…

Probability · Mathematics 2023-03-03 Alexander Stolyar

We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuous limit for the macroscopic behavior of the system, the…

Probability · Mathematics 2023-09-11 Pierre-Emmanuel Jabin , Datong Zhou

In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field…

Probability · Mathematics 2024-09-27 Camilo Hernández , Ludovic Tangpi

This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…

Probability · Mathematics 2022-05-26 Jian Song , Meng Wang

The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…

Analysis of PDEs · Mathematics 2025-06-25 Elisabetta Brocchieri , Lucilla Corrias

This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…

Dynamical Systems · Mathematics 2017-07-20 Dang H. Nguyen , Nguyen H. Du , George Yin