Mean cover time of one-dimensional persistent random walks

TL;DR

This paper derives the exact mean cover time for one-dimensional persistent random walks, a model with short-range memory, on finite lattices with different boundary conditions.

Contribution

It provides the first exact analytical expression for the mean cover time of persistent random walks in one dimension.

Findings

Exact mean cover time formulas for periodic and reflecting boundaries

Analytical results for persistent random walks with short-range memory

Enhanced understanding of cover times in correlated random walk models

Abstract

The cover time is defined as the time needed for a random walker to visit every site of a confined domain. Here, we focus on persistent random walks, which provide a minimal model of random walks with short range memory. We derive the exact expression of the mean cover time of a one-dimensional lattice by such a persistent random walk, both for periodic and reflecting boundary conditions.