Interacting particle systems with long-range interactions: scaling limits and kinetic equations
Alessia Nota
Università degli studi dell’Aquila, ItalyJuan J.L. Velázquez
Universität Bonn, GermanyRaphael Winter
Université de Lyon, Villeurbanne, France
![Interacting particle systems with long-range interactions: scaling limits and kinetic equations cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rlm-volume-32-issue-2.png&w=3840&q=90)
Abstract
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential and scaling limit. Our focus in this paper is on particle systems with long-range interactions. The derivation here is formal, but it provides an interpretation of particle systems as the motion of a particle in a random force field with a friction term which is due to the interaction with the surrounding particles. Some of the technical details of this method are discussed in the companion paper [50].
Cite this article
Alessia Nota, Juan J.L. Velázquez, Raphael Winter, Interacting particle systems with long-range interactions: scaling limits and kinetic equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 2, pp. 335–377
DOI 10.4171/RLM/939