Interacting particle systems with long-range interactions: scaling limits and kinetic equations

  • Alessia Nota

    Università degli studi dell’Aquila, Italy
  • Juan J. L. Velázquez

    Universität Bonn, Germany
  • Raphael Winter

    Université de Lyon, Villeurbanne, France
Interacting particle systems with long-range interactions: scaling limits and kinetic equations cover
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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