Sensitivity of the frog model to initial conditions

Abstract

The frog model is an interacting particle system on a graph. Active particles perform independent simple random walks, while sleeping particles remain inert until visited by an active particle. Some number of sleeping particles are placed at each site sampled independently from a certain distribution, and then one particle is activated to begin the process. We show that the recurrence or transience of the model is sensitive not just to the expectation but to the entire distribution. This is in contrast to closely related models like branching random walk and activated random walk.

References in corpus (6)

• Effects of Fluctuations on Propagating Fronts
• From transience to recurrence with Poisson tree frogs
• Recurrence and transience for the frog model on trees
• Stochastic orders and the frog model
• The critical density for the frog model is the degree of the tree
• Universality and Sharpness in Absorbing-State Phase Transitions

Cited by in corpus (2)

• Activated Random Walks on ${\mathbb{Z}}^d$
• Diffusion-limited annihilating systems and the increasing convex order