Abstract:
The Abelian sandpile was discovered more than thirty years ago, independently in Statistical Physics and Combinatorics. It has strong connections to Potential Theory. The related rotor-router model offers an alternative approach to fair division of indivisible particles. We survey the progress made on describing scaling limits of these models on Euclidean lattices as the mesh size goes to zero, starting with the circularity result for internal DLA by Lawler-Bramson-Griffeath, through our own work with Levine on rotor-routers and multiple sources, and the remarkable results of Pegden and Smart, who overcame the obstacle of lattice dependence. The mystery of dimension reduction in sandpiles is now partly understood in recent work of Bou-Rabee. These models yield attractive simulations and many intriguing open problems.
(Lecture based on forthcoming book with Ahmed Bou-Rabee and Lionel Levine)
Biography:
Yuval Peres obtained his PhD in 1990 from the Hebrew University, Jerusalem. He was a postdoctoral fellow at Stanford and Yale, and was then a Professor of Mathematics and Statistics in Jerusalem and in Berkeley. Later, he was a Principal researcher at Microsoft. Yuval has published more than 350 papers in most areas of probability theory, including random walks, Brownian motion, percolation, and random graphs. He has co-authored books on Markov chains, probability on graphs, game theory and Brownian motion, which can be found at https://www.yuval-peres-
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.