## EVENT DETAILS AND ABSTRACT

**Analysis and Probability Seminar**
**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.

**Date:** Monday, February 13, 2006

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Elton P. Hsu

**Contact email:** elton@math.northwestern.edu

**Contact Phone:** 847-491-8541

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