Recurrence for the frog model with drift on $\mathbb{Z}^d$

TL;DR

This paper establishes a recurrence criterion for the frog model on multi-dimensional integer lattices with drift, providing insights into how initial configurations and drift influence the model's recurrence behavior.

Contribution

It introduces a new recurrence criterion for the frog model with drift on b^d, advancing understanding of its long-term behavior under various initial conditions.

Findings

Recurrence depends on initial frog configuration and drift strength.

Criteria applicable to b^d with i.i.d. initial sleeping frogs.

Results extend previous models without drift.

Abstract

In this paper we present a recurrence criterion for the frog model on $\mathbb{Z}^d$ with an i.i.d. initial configuration of sleeping frogs and such that the underlying random walk has a drift to the right.