Random walks on discrete Abelian groups

TL;DR

This paper establishes precise conditions under which random walks on subgroups of the rational numbers are recurrent, advancing understanding of stochastic processes on algebraic structures.

Contribution

It provides necessary and sufficient criteria for recurrence of random walks on subgroups of 5, a novel result in the study of stochastic processes on algebraic groups.

Findings

Derived conditions for recurrence on subgroups of 5

Characterized when random walks are recurrent or transient

Extended previous results to arbitrary subgroups of 5

Abstract

In the present paper we find necessary and sufficient conditions for recurrence of random walks on arbitrary subgroups of the group of rational numbers $\mathbb{Q}$.