The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
We consider the activated random walk model on general vertex-transitive graphs. A central question for this model is whether the critical density \mu_c for sustained activity is strictly between 0 and 1. It was known that \mu_c>0 on Z^d, d\geq 1, and that \mu_c<1 on Z for small enough sleeping rate. We show that \mu_c\to 0 as \lambda \to 0 in all transient graphs, implying that \mu_c<1 for small enough sleeping rate. We also show that \mu_c<1 for any sleeping rate in any graph in which simple random walk has positive speed. Furthermore, we prove that \mu_c>0 in any amenable graph, and that \mu_c\ in(0,1) for any sleeping rate on regular trees.
Biography:
Alexandre Stauffer is a researcher at the University of Bath, UK. He got a Ph.D. from the University of California, Berkeley, and was a post-doc at Microsoft Research, Redmond, and Universita Roma Tre. His research is in the area of discrete probability, including interacting particle systems and Markov chain mixing time.