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Related papers: Mean-field limits \`a la Tanaka and large deviatio…

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There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…

Probability · Mathematics 2020-10-15 Daniel Remenik

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

This paper investigates the limit behavior of Markov Decision Processes (MDPs) made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted…

Probability · Mathematics 2009-06-10 Nicolas Gast , Bruno Gaujal

We investigate the monitored dynamics of many-body quantum systems in which projective measurements of extensive operators are alternated with unitary evolution. Focusing on mean-field models characterized by all-to-all interactions, we…

Statistical Mechanics · Physics 2025-12-05 Luca Capizzi , Riccardo Travaglino

We study some systems of interacting fields whose evolution is given by some singular stochastic partial differential equations of mean field type. We provide a robust setting for their study and prove a well-posedness result and a…

Probability · Mathematics 2026-04-15 I. Bailleul , N. Moench

We present a Mean Field Game approach to obtain the rate function for the empirical measure of interacting particles under McKean-Vlasov dynamics. Although the result is well known, our approach relies on PDE methods and provides another…

Analysis of PDEs · Mathematics 2023-10-13 Nikiforos Mimikos-Stamatopoulos

The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the…

Condensed Matter · Physics 2007-05-23 B. Kramer , D. Belitz , M. Batsch

We study infinite-horizon Markov Decision Processes (MDPs) with a continuum of heterogeneous agents interacting through a common noise, without assuming exchangeability. We introduce the framework of Conditional Non-Exchangeable Mean Field…

Optimization and Control · Mathematics 2026-03-03 Samy Mekkaoui , Huyên Pham

Building on the line of work [DIRT15a], [DIRT15b], [NS17a], [DT17], [HLS18], [HS18] we continue the study of particle systems with singular interaction through hitting times. In contrast to the previous research, we (i) consider very…

Probability · Mathematics 2019-09-26 Sergey Nadtochiy , Mykhaylo Shkolnikov

A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of discrete solutions and a discrete entropy production…

Numerical Analysis · Mathematics 2019-11-27 Ansgar Jüngel , Antoine Zurek

We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…

Probability · Mathematics 2011-10-25 A. Manita , V. Shcherbakov

We consider a general interacting particle system with interactions on a random graph, and study the large population limit of this system. When the sequence of underlying graphs converges to a graphon, we show convergence of the…

Probability · Mathematics 2024-10-16 Carla Crucianelli , Ludovic Tangpi

Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…

Statistical Mechanics · Physics 2023-05-03 Leticia F. Cugliandolo

A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long range…

Probability · Mathematics 2012-10-02 Mustapha Mourragui , Enza Orlandi

We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction…

Nuclear Theory · Physics 2008-11-26 T. Niksic , D. Vretenar , G. A. Lalazissis , P. Ring

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…

Statistical Mechanics · Physics 2009-10-31 Peter J. Klinko , Bruce N. Miller

In this paper we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in~\cite{DuncanPavliotis2016}. We…

Statistical Mechanics · Physics 2018-01-17 S. N. Gomes , G. A. Pavliotis

The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially…

Probability · Mathematics 2022-09-01 Xuda Ye , Zhennan Zhou

In this work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belongs to a suitable $L_t^q-L_x^p$ space. Contrary to the large…

Probability · Mathematics 2023-07-19 Milica Tomašević

In this work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory.…

Analysis of PDEs · Mathematics 2025-08-05 Tau Shean Lim , Chao Dun Teoh