The range of once-reinforced random walk on the half-line

TL;DR

This paper studies a once-reinforced random walk on the half-line, analyzing the long-term behavior of the moments of its range to understand its probabilistic properties.

Contribution

It provides a comprehensive analysis of the limiting behaviors of all moments of the range for the once-reinforced random walk on the half-line.

Findings

Derived the limiting behaviors of all moments of the range.

Established new probabilistic properties of the reinforced random walk.

Enhanced understanding of the walk's long-term distribution.

Abstract

In this paper, we consider a once-reinforced random walk on the half-line, and give the limiting behaviors of all the moments of its range.