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We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…

Probability · Mathematics 2026-01-15 Kuldeep Guha Mazumder

We study simple nonequilibrium distributions describing a classical gas of particles interacting via a pair potential ${\phi}(x/{\epsilon})$, in the Boltzmann-Grad scaling ${\epsilon} \rightarrow 0$. We establish bounds for truncated…

Mathematical Physics · Physics 2024-06-17 Andrea Di Stefano , Sergio Simonella , Raphael Winter

In this note we continue the study of nonlocal interaction dynamics on a sequence of infinite graphs, extending the results of [Esposito et. al 2023+] to an arbitrary number of species. Our analysis relies on the observation that the graph…

Analysis of PDEs · Mathematics 2023-07-03 Antonio Esposito , Georg Heinze , Jan-Frederik Pietschmann , André Schlichting

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…

Statistical Mechanics · Physics 2018-04-05 Niels Buhl

It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…

Statistical Mechanics · Physics 2016-01-13 Tiziano Squartini , Joey de Mol , Frank den Hollander , Diego Garlaschelli

A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework…

Probability · Mathematics 2024-10-10 Louis-Pierre Chaintron

Graphene is known to possess strong optical nonlinearity. Its nonlinear response can be further enhanced by graphene plasmons. Here, we report a novel nonlinear electro-absorption effect observed in nanostructured graphene due to excitation…

Mesoscale and Nanoscale Physics · Physics 2018-02-14 D. Kundys , B. Van Duppen , O. P. Marshall , F. Rodriguez , I. Torre , A. Tomadin , M. Polini , A. N. Grigorenko

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Probability · Mathematics 2025-06-09 Pascal Bianchi , Walid Hachem , Victor Priser

In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…

Probability · Mathematics 2022-12-06 Maxime Hauray , Etienne Pardoux , Yen V. Vuong

Consider a stationary Poisson process $\eta$ in the $d$-dimensional Euclidean or hyperbolic space and construct a random graph with vertex set $\eta$ as follows. First, each point $x\in\eta$ is connected by an edge to its nearest neighbour,…

Probability · Mathematics 2024-11-04 Holger Sambale , Christoph Thäle , Tara Trauthwein

We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the…

Probability · Mathematics 2009-08-14 Glauco Valle

We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…

Probability · Mathematics 2024-11-13 Patrick van Meurs , Kenkichi Tsunoda , Lu Xu

In the case of compact quantum graphs, many-particle models with singular two-particle interactions where introduced in [arXiv:1207.5648, arXiv:1112.4751] to provide a paradigm for further studies on many-particle quantum chaos. In this…

Mathematical Physics · Physics 2018-01-04 Joachim Kerner , Tobias Mühlenbruch

An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of…

Probability · Mathematics 2020-06-03 Franco Flandoli , Marta Leocata , Cristiano Ricci

This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal…

Probability · Mathematics 2026-04-17 Daniel Lacker , Lane Chun Yeung , Fuzhong Zhou

There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical…

Mathematical Physics · Physics 2022-05-03 Vassili N. Kolokoltsov

The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant…

Mathematical Physics · Physics 2012-07-12 Yves Elskens

We generalize the notion of quasirandom which concerns a class of equivalent properties that random graphs satisfy. We show that the convergence of a graph sequence under the spectral distance is equivalent to the convergence using the…

Combinatorics · Mathematics 2013-11-06 Fan Chung

Graphons have traditionally served as limit objects for dense graph sequences, with the cut distance serving as the metric for convergence. However, sparse graph sequences converge to the trivial graphon under the conventional definition of…

Signal Processing · Electrical Eng. & Systems 2023-09-12 Xingchao Jian , Feng Ji , Wee Peng Tay

We prove sharp estimates for the mean-field limit of weakly interacting diffusions with repulsive logarithmic interaction in arbitrary dimension. More precisely, we show that the associated partition function is uniformly bounded in the…

Probability · Mathematics 2025-06-30 Matias G. Delgadino , Rishabh S. Gvalani