Limit theorems for random walks on a strip in subdiffusive regime

TL;DR

This paper investigates the long-term behavior of occupation and hitting times for a transient random walk on a strip in a sub-diffusive regime, solving a longstanding problem for bounded jumps on a 1D lattice.

Contribution

It provides a detailed analysis of occupation times in a quenched environment and characterizes the asymptotics of random walks with bounded jumps, addressing open questions in the field.

Findings

Asymptotic behavior of occupation times characterized

Hitting times exhibit identical asymptotics

Resolved a longstanding problem for 1D bounded jump walks

Abstract

We study the asymptotic behaviour of occupation times of a transient random walk in quenched random environment on a strip in a sub-diffusive regime. The asymptotic behaviour of hitting times, which is a more traditional object of study, is the exactly same. As a particular case, we solve a long standing problem of describing the asymptotic behaviour of a random walk with bounded jumps on a one-dimensional lattice