The speed of frogs with drift on $\mathbb{Z}$

Abstract

In this article we consider the frog model with drift on $\mathbb{Z}$ and investigate the behaviour of the cloud of the frogs. In particular, we show that the speed of the minimum equals the speed of a single frog and prove some properties of the speed of the maximum. In addition, we show a limit theorem for the empirical distribution.

References in corpus (3)

• From transience to recurrence with Poisson tree frogs
• On the range of the transient frog model on Z
• A zero-one law for recurrence and transience of frog processes

Cited by in corpus (2)

• Deviation bounds for the first passage time in the frog model
• A zero-one law for recurrence and transience of frog processes