Mean first-passage and residence times of random walks on asymmetric disordered chains

TL;DR

This paper derives exact solutions for mean first-passage and residence times of asymmetric random walks on disordered chains, analyzing the effects of boundary conditions and the interplay between asymmetry and disorder.

Contribution

It provides algebraic solutions for these times in disordered chains, considering different boundary conditions and the combined effects of asymmetry and disorder.

Findings

Exact solutions for mean first-passage times under disorder

Analysis of boundary condition effects on residence times

Insights into asymmetry and disorder interplay

Abstract

An algebraic derivation is presented which yields the exact solution of the mean first-passage and mean residence times of a one-dimensional asymmetric random walk for quenched disorder. Two models of disorder are analytically treated. Both, absorbing-absorbing and reflecting-absorbing boundaries are considered. Particularly, the interplay between asymmetry and disorder is studied.