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Related papers: Sequential propagation of chaos

200 papers

We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as…

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

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

This work addresses the propagation of chaos properties in a class of moderately interacting particle systems for the approximation of singular kinetic McKean-Vlasov SDEs driven by alpha-stable processes.

Analysis of PDEs · Mathematics 2026-02-16 Zimo Hao , Jean-Francois Jabir , Stéphane Menozzi , Michael Röckner , Xicheng Zhang

We prove propagation of chaos at explicit polynomial rates in Wasserstein distance W_2 for Kac's N-particle system associated with the spatially homogeneous Boltzmann equation for Maxwell molecules, with and without cutoff. Our approach is…

Mathematical Physics · Physics 2017-12-27 Roberto Cortez , Joaquin Fontbona

In this paper we study Kac's 1D particle system, consisting of the velocities of $N$ particles colliding at constant rate and randomly exchanging energies. We prove uniform (in time) propagation of chaos in Wasserstein distance with…

Probability · Mathematics 2016-12-21 Roberto Cortez

A system of interacting multiclass finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-colors nodes. The interaction is local and described through…

Probability · Mathematics 2021-08-23 Donald A. Dawson , Ahmed Sid-Ali , Yiqiang Q. Zhao

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

We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…

Probability · Mathematics 2019-07-18 Nils Detering , Jean-Pierre Fouque , Tomoyuki Ichiba

We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic…

Probability · Mathematics 2016-05-05 Roberto Cortez , Joaquin Fontbona

We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…

Analysis of PDEs · Mathematics 2026-03-16 Myeongju Chae , Young-Pil Choi

In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…

Numerical Analysis · Mathematics 2023-05-30 Qian Guo , Jie He , Lei Li

We develop a mean-field theory for large, non-exchangeable particle (agent) systems where the states and interaction weights co-evolve in a coupled system of SDEs. A first main result is the establishment of the propagation of…

Probability · Mathematics 2025-12-30 Datong Zhou

The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…

Probability · Mathematics 2015-10-13 Marie-Noémie Thai

We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…

Analysis of PDEs · Mathematics 2017-05-12 Young-Pil Choi , Samir Salem

We consider a general McKean-Vlasov stochastic differential equation driven by a rotationally invariant $\alpha$-stable process on $\mathbb{R}^d$ with $\alpha \in (1,2)$. We assume that the diffusion coefficient is the identity matrix and…

Analysis of PDEs · Mathematics 2024-01-29 Thomas Cavallazzi

As an enhanced version of existing results on Kac's propagation of chaos, which describes the convergence of mean-field particle systems to a system of independent McKean-Vlasov particles as the number of particles tends to infinity, we…

Probability · Mathematics 2026-05-12 Xiao-Yu Zhao

We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions. Our main examples are interactions governed by convex potentials and models on the torus with small interactions. We show that…

Probability · Mathematics 2023-01-23 Daniel Lacker , Luc Le Flem

We derive two estimates for the deviation of the $N$-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our…

Probability · Mathematics 2019-05-23 Daniel Heydecker

A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated…

Probability · Mathematics 2024-08-13 Daniel Hernández-Hernández , Joshué Helí Ricalde-Guerrero

We consider a $N$-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system.…

Analysis of PDEs · Mathematics 2018-08-01 José A. Carrillo , Young-Pil Choi , Samir Salem