Run-and-tumble particles in slit geometry as a splitting probability problem

TL;DR

This paper reinterprets the behavior of run-and-tumble particles in slit geometries as a splitting probability problem, enabling new analytical approaches and insights beyond traditional differential equation methods.

Contribution

It introduces a novel integral equation formulation for analyzing run-and-tumble particles, extending analytical tractability to higher dimensions.

Findings

Integral equation formulation for splitting probability

Analytical insights into higher-dimensional systems

Enhanced understanding of particle confinement dynamics

Abstract

Run-and-tumble particles confined between two walls seem like a simple enough problem to possess analytical tractability. Yet up to date, no satisfactory analysis is available for dimensions higher than one. This work contributes to the theoretical understanding of this system by reinterpreting it as a splitting probability problem. Such reinterpretation permits us to formulate the problem as the integral equation, rather than a more standard differential equation based on the Fokker-Planck equation. In addition to providing an analogy with another phenomenon, the reinterpretation permits a new type of analysis, yields useful results, and offers some analytical tractability.