The stochastic acceleration problem in two dimensions

TL;DR

This paper studies the behavior of a particle in a 2D mixing potential, showing its momentum converges to Brownian motion on a circle, extending previous results from higher dimensions.

Contribution

It provides a new limit theorem for the stochastic acceleration problem specifically in two dimensions, complementing existing higher-dimensional results.

Findings

Momentum converges to Brownian motion on a circle in 2D.

Extends the stochastic acceleration limit theorem to two dimensions.

Complements previous results valid for dimensions d ≥ 3.

Abstract

We consider the motion of a particle in a two-dimensional spatially homogeneous mixing potential and show that its momentum converges to the Brownian motion on a circle. This complements the limit theorem of Kesten and Papanicolaou \cite{KP} proved in dimensions $d\ge 3$.