We study the a case of the A+B interacting particle system on Z^d known as the frog model. At each site there are initially a Poisson number of sleeping frogs. When an active frog visits a site, all frogs there wake up, perform a random walk for some time, and die. In this work, our random walks are heavy tailed. We connect this model with long range percolation, and derive estimates for the hitting time of a vertex and the cover time of the torus. We also study the nature of the phase survival transition.

Joint with Jonathan Hermon, Yuliang Shi, and Daniel de la Riva.