# The range of once-reinforced random walk in one dimension

## TL;DR

This paper investigates the properties of once-reinforced random walk on the integer lattice, deriving comprehensive limit results for all moments of its range through advanced Tauberian techniques.

## Contribution

It provides the first detailed moment analysis of the range of ORRW in one dimension using Tauberian theory, expanding understanding of reinforced random walks.

## Key findings

- Derived limit results for all moments of the range
- Applied Tauberian theory to reinforced random walk
- Enhanced theoretical understanding of ORRW behavior

## Abstract

We study once-reinforced random walk (ORRW) on $\mathbb Z$. For this model, we derive limit results on all moments of its range using Tauberian theory.