The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field

TL;DR

This paper investigates the many-body dynamics of particles interacting via a wave field, deriving the Vlasov limit and analyzing fluctuations, thus extending the understanding of such coupled particle-wave systems.

Contribution

It establishes the Vlasov continuum limit and a central limit theorem for fluctuations in a particle-wave interaction model, advancing the mathematical understanding of these systems.

Findings

Vlasov limit obtained as a weak law of large numbers.

Central limit theorem established for fluctuations.

Provides rigorous mathematical framework for particle-wave interactions.

Abstract

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.