Department of Mathematics,
University of California San Diego
****************************
Math 288 - Probability Seminar
Lionel Levine
Cornell University
Threshold state of the abelian sandpile
Abstract:
A sandpile on a graph is an integer-valued function on the vertices. It evolves according to local moves called topplings. Some sandpiles stabilize after a finite number of topplings, while others topple forever. For any sandpile $s_0$ if we repeatedly add a grain of sand at an independent random vertex, we eventually reach a "threshold state'' $s_T$ that topples forever. Poghosyan, Poghosyan, Priezzhev and Ruelle conjectured a precise value for the expected amount of sand in $s_T$ in the limit as $s_0$ tends to negative infinity. I will outline how this conjecture was proved by means of a Markov renewal theorem.
Host: Todd Kemp
November 12, 2015
9:00 AM
AP&M 6402
****************************