Recurrence and transience of critical branching processes in random environment with immigration and an application to excited random walks

TL;DR

This paper develops criteria to determine when critical branching processes with immigration in random environments are recurrent or transient, and applies these results to analyze a related excited random walk model.

Contribution

It introduces new recurrence and transience criteria for critical branching processes with immigration in random environments and applies them to excited random walks with cookies.

Findings

Established criteria for recurrence and transience in branching processes

Applied criteria to excited random walks with drift-inducing cookies

Provided insights into the behavior of random walks in disturbed environments

Abstract

We establish recurrence and transience criteria for critical branching processes in random environment with immigration. These results are then applied to discuss recurrence and transience of a recurrent random walk in a random environment on Z that will be disturbed by cookies inducing a drift to the right of strength 1.