First-passage times for random walks in bounded domains

TL;DR

This paper introduces a new computational approach for calculating first-passage times in bounded domains, providing accurate moments, extensions to multiple targets and Brownian motion, with validation and relevance to confined diffusion systems.

Contribution

A novel computational method for first-passage times in bounded lattices, including moments, multiple targets, and continuous Brownian motion extensions.

Findings

Validated expressions for all moments of first-passage times.

Extended analysis to multiple targets and Brownian motion.

Discussed the method's range of validity.

Abstract

We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical simulations. Their range of validity is discussed. We also consider the case of a starting site and two targets. In addition, we present the extension to continuous Brownian motion. These results are of great relevance to any system involving diffusion in confined media.