Random walks systems with finite lifetime on $ \bbZ $

Elcio Lebensztayn, Fabio Machado, Mauricio Zuluaga

Published 2015-09-22Version 1

We consider a non-homogeneous random walks system on $\bbZ$ 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.