Motion in a Random Force Field

TL;DR

This paper studies the long-term behavior of a particle moving in a high-dimensional random force field generated by a Poisson process, focusing on cases with large initial velocities.

Contribution

It provides a detailed asymptotic analysis of particle motion in a random isotropic force field in dimensions four and higher, under large initial velocities.

Findings

Asymptotic behavior characterized for large initial velocities

Motion described in high-dimensional Poisson force fields

Results applicable to isotropic random force environments

Abstract

We consider the motion of a particle in a random isotropic force field. Assuming that the force field arises from a Poisson field in $\mathbb{R}^d$, $d \geq 4$, and the initial velocity of the particle is sufficiently large, we describe the asymptotic behavior of the particle.