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Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts…

Statistics Theory · Mathematics 2025-11-04 Zhou Fan , Justin Ko , Bruno Loureiro , Yue M. Lu , Yandi Shen

We study the evolution of two-point correlation functions of one-dimensional Bose-Hubbard model in the semiclassical regime in the framework of Truncated Wigner Approximation (TWA) with quantum jumps as first-order corrections. At early…

Quantum Physics · Physics 2025-07-04 Dragan Marković , Mihailo Čubrović

We analyze the propagation of experimentally relevant two-particle correlations for one-dimensional interacting bosons, and give evidence that many-body chaos induces the emergence of an effective diffusive regime for the fully coherent…

Quantum Physics · Physics 2025-02-12 Óscar Dueñas , David Peña , Alberto Rodríguez

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

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

Nonreciprocal interactions, in which action-reaction symmetry is broken, provide a powerful route to collective dynamics that cannot be captured by equilibrium free-energy minimisation. Here, we introduce and analyse a two-species…

Statistical Mechanics · Physics 2026-05-11 Arjun R , Pratyush Prakash Patra , A. V. Anil Kumar

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 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

In this article, we are interested in the behavior of a fully connected network of $N$ neurons, where $N$ tends to infinity. We assume that the neurons follow the stochastic FitzHugh-Nagumo model, whose specificity is the non-linearity with…

Probability · Mathematics 2024-02-14 Laetitia Colombani , Pierre Le Bris

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

We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they…

Chaotic Dynamics · Physics 2015-06-05 Timo Hartmann , Juan-Diego Urbina , Klaus Richter , Peter Schlagheck

We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the…

Probability · Mathematics 2025-11-06 Fan Chen , Zhenjie Ren , Songbo Wang

We provide an estimation of the dissipation of the Wasserstein 2 distance between the law of some interacting $N$-particle system, and the $N$ times tensorized product of solution to the corresponding limit nonlinear conservation law. It…

Analysis of PDEs · Mathematics 2018-10-23 Samir Salem

We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the exponential convergence of the mean field dynamics and then show…

Probability · Mathematics 2024-02-09 Fan Chen , Yiqing Lin , Zhenjie Ren , Songbo Wang

In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…

Probability · Mathematics 2022-07-14 Yun Li , Longjie Xie

We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution…

Probability · Mathematics 2010-08-30 Mykhaylo Shkolnikov

We study the evolution of a pathogen with two allelic types infecting a population of hosts, where within-host type frequencies evolve in discrete time. Our framework is built on a two-parameter family of transition kernels on [0,1], which…

Probability · Mathematics 2025-11-19 Fernando Cordero , Christian Jorquera , Héctor Olivero , Leonardo Videla

This paper focuses on the numerical stability of stochastic McKean-Vlasov equations (SMVEs) via the stochastic particle method. Firstly, the long-time propagation of chaos in the mean-square sense is obtained, and the almost sure…

Numerical Analysis · Mathematics 2025-08-04 Zhuoqi Liu , Shuaibin Gao , Chenggui Yuan , Qian Guo

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…

Probability · Mathematics 2014-01-15 Stéphane Mischler , Clément Mouhot , Bernt Wennberg

We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…

Analysis of PDEs · Mathematics 2025-12-15 Lucas M. Fix , Gianna Götzmann , Malte A. Peter , Jan-F. Pietschmann