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We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…

Analysis of PDEs · Mathematics 2026-01-13 Nathalie Ayi

In this paper, we present a rigorous derivation of the mean-field limit for a moderately interacting particle system in $\R^d$ $(d\geq 2)$. For stochastic initial data, we demonstrate that the solution to the interacting particle model,…

Analysis of PDEs · Mathematics 2024-07-08 Jinhuan Wang , Mengdi Zhuang , Hui Huang

Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution operator displays fluctuations around its expectation. The recently developed pathwise theory of fluctuations in…

Analysis of PDEs · Mathematics 2021-12-01 Mitia Duerinckx , Julian Fischer , Antoine Gloria

Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…

Probability · Mathematics 2013-08-19 Amarjit Budhiraja , Zhen-Qing Chen

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…

Probability · Mathematics 2020-06-02 Carsten Chong , Claudia Klüppelberg

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate…

Disordered Systems and Neural Networks · Physics 2017-11-01 Yevgeny Bar Lev , Dante M. Kennes , Christian Klöckner , David R. Reichman , Christoph Karrasch

This note is a companion article to the recent paper L\"ocherbach, Loukianova, Marini (2024). We consider mean field systems of interacting particles. Each particle jumps with a jump rate depending on its position. When jumping, a…

Probability · Mathematics 2024-07-02 Dasha Loukianova , Eva Löcherbach

Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion…

Analysis of PDEs · Mathematics 2021-10-13 Li Chen , Esther S. Daus , Alexandra Holzinger , Ansgar Jüngel

We provide an existence result for stationary fractional mean field game systems, with fractional exponent greater than 1/2. In the case in which the coupling is a nonlocal regularizing potential, we obtain existence of solutions under…

Analysis of PDEs · Mathematics 2017-05-30 Annalisa Cesaroni , Marco Cirant , Serena Dipierro , Matteo Novaga , Enrico Valdinoci

A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…

Analysis of PDEs · Mathematics 2021-09-20 Li Chen , Alexandra Holzinger , Ansgar Jüngel , Nicola Zamponi

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…

Probability · Mathematics 2022-04-21 Vassili Kolokoltsov , Marianna Troeva

We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary…

Analysis of PDEs · Mathematics 2020-12-23 Sylvia Serfaty , appendix with Mitia Duerinckx

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

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

Analysis of PDEs · Mathematics 2019-09-25 Jose A. Carrillo , Edgard A. Pimentel , Vardan K. Voskanyan

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…

Analysis of PDEs · Mathematics 2016-05-31 Fernando A. Morales , Daniel E. Restrepo

In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle…

Chemical Physics · Physics 2024-05-01 Anthony Scemama , Andreas Savin

We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems…

Mathematical Physics · Physics 2014-02-19 Boris Pawilowski , Quentin Liard

We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…

Analysis of PDEs · Mathematics 2012-05-22 Ondrej Budáč , Michael Herrmann , Barbara Niethammer , Andrej Spielmann

We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperplane interfaces with oblique penetration. We show that this…

Probability · Mathematics 2024-02-05 Olga Aryasova , Ilya Pavlyukevich , Andrey Pilipenko

We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $\phi$ and a non-linear coupling of velocities given by the power…

Analysis of PDEs · Mathematics 2026-01-01 Vinh Nguyen , Roman Shvydkoy , Changhui Tan