Exact expressions of mean first-passage times and splitting probabilities for random walks in bounded rectangular domains

TL;DR

This paper derives exact formulas for mean first-passage times and splitting probabilities of random walks in bounded rectangular domains with various boundary conditions and absorbing targets.

Contribution

It provides explicit expressions for mean first-passage times and splitting probabilities in rectangular domains with reflecting or periodic boundaries, considering one or two absorbing targets.

Findings

Exact formulas for mean first-passage times are obtained.

Explicit splitting probabilities are derived for different boundary conditions.

Results apply to random walks with multiple absorbing targets.

Abstract

We give exact and explicit expressions of mean first-passage times for random walks in a rectangular domain, in both cases of reflecting boundary conditions and periodic boundary conditions. The situations with one or two absorbing targets are considered.