On homogeneous and oscillating random walks on the integers

TL;DR

This paper simplifies classical results on the recurrence of homogeneous and oscillating random walks on integers, connecting them with renewal theory and providing clearer insights into their behavior.

Contribution

It offers simplified proofs of classical recurrence results and explores links between random walks and renewal theory.

Findings

Simplified classical recurrence criteria for random walks

Established connections with renewal theory

Enhanced understanding of oscillating walk behavior

Abstract

Considering homogeneous and oscillating random walks on the integers, we simplify classical works on recurrence of Spitzer and Kemperman, respectively. Some links with renewal theory are discussed.