Interacting particle systems with long-range interactions: scaling limits and kinetic equations
Mathematical Physics
2020-12-10 v2 math.MP
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 [47].
Keywords
Cite
@article{arxiv.2003.11605,
title = {Interacting particle systems with long-range interactions: scaling limits and kinetic equations},
author = {Alessia Nota and Juan J. L. Velázquez and Raphael Winter},
journal= {arXiv preprint arXiv:2003.11605},
year = {2020}
}
Comments
37 pages; shorter version