The Richardson model in a random environment

Abstract

Let ξ t: Z d→s{0,2} be such that all coordinates are independent and, in each coordinate, 2 changes to 0 at rate β and 0 changes to 2 at rate 1. A family of particles (1's) move in the space occupied by 0's like Richardson model, i.e., a 0 becomes 1 at a rate proportional to 1-occupied neighbors. We prove the phase transition phenomena for the coexistence of 0's, 1's and 2's.