## EVENT DETAILS AND ABSTRACT

**Probability Seminar**
**Title:** Two-type diffusion limited annihilating systems

**Speaker:** Toby Johnson

**Speaker Info:** CUNY

**Brief Description:**

**Special Note**:

**Abstract:**

In the two-type DLAS process, we place particles of two types on a graph and let them move randomly. When two particles of opposite type meet each other, both annihilate. The most basic question is to determine the density of particles at time t. When the two particle types jump at the same rate and have equal initial density, Bramson and Lebowitz proved that on the d-dimensional lattice, the density decays at rate t^(-d/4) for d=1, 2, 3 and at rate t^(-1) when d is 4 or greater, which was long conjectured by physicists. When the particle types jump at different rates, much less is known. We prove some results in these cases on lattices and on directed trees. The process on trees has some resemblance to the Derrida-Retaux hierarchical renormalization model. Joint work with Michael Damron, Matthew Junge, Hanbaek Lyu, and David Sivakoff.

**Date:** Tuesday, February 18, 2020

**Time:** 3:00PM

**Where:** Lunt 107

**Contact Person:** Julian Gold

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

**Contact Phone:**

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