Random walks systems with finite lifetime on $\mathbb{Z}$

Abstract

We consider a non-homogeneous random walks system on $\mathbb{Z}$ in which each active particle performs a nearest neighbor random walk and activates all inactive particles it encounters up to a total amount of $L$ jumps. We present necessary and sufficient conditions for the process to survive, which means that an infinite number of random walks become activated.

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References in corpus (1)

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

Cited by in corpus (1)

• Laws of large numbers for the frog model on the complete graph