Coexistence in discrete time multi-type competing frog models

We study coexistence in discrete time multi-type frog models. We first show that for two types of particles on Zd, for d ≥ 2, for any jumping parameters p1, p2 ∈ (0, 1], coexistence occurs with positive probability for sufficiently rich deterministic initial configuration. We extend this to the case of random distribution of initial particles. We study the question of coexistence for multiple types and show positive probability coexistence of 2d types on Zd for rich enough initial configuration. We also show an instance of infinite coexistence on Zd for d ≥ 3 provided we have sufficiently rich initial configuration.