Random walk in a rotational environment

TL;DR

This paper studies a particle's random walk in a rotating 3D space, analyzing how collisions influence its long-term deterministic movement derived from the space's rotation.

Contribution

It introduces a model of a particle's random walk in a rotating environment and characterizes its asymptotic behavior and limit movement.

Findings

The particle's long-term movement becomes deterministic influenced by space rotation.

Random collisions lead to predictable asymptotic behavior.

The model explains how space rotation affects particle dynamics.

Abstract

We define a random walk of a particle in $\mathbb{R}^3$ where the space is rotating. The particle is not glued to the space and will collide with it at random times, resulting in changes in its velocity and direction. After many collisions, the random walk starts to have some asymptotic behaviors inherited from the movement of space. The paper will find the limit movement of the particle, and explain how the randomness of the random walk gives rise to the particle asymptotic deterministic movement.