EVENT DETAILS AND ABSTRACT

Title: Coexistence for Richardson type competing spatial growth models
Speaker: Professor Chris Hoffman
Speaker Info: University of Washington
Brief Description:
Special Note:
Abstract:

In the Richardson growth model the vertices in Z^d can take on three possible states 0,1, and 2. Vertices in states 1 and 2 remain in their states forever, while vertices in state 0 which are adjacent to a vertex in state 1 (or state 2) can switch to state 1 (or state 2). We think of the vertices in states 1 and 2 as infected with one of two infections while the vertices in state 0 are considered uninfected. We start the models with a single vertex in state 1 and a single vertex is in state 2. We show that with positive probability state 1 reaches an infinite number of vertices and state 2 also reaches an infinite number of vertices. The key tool is applying the ergodic theorem to stationary first passage percolation.