General Events - Department of Mathematics

Title: Stochastic growth models 

Abstract: In the last third of the 20th century probability theory expanded from stochastic processes indexed by one-dimensional time to stochastic models with new types of complex spatial dependencies. Examples include random growth models, random trees and graphs, percolation, random paths in a random medium, and interacting particle systems.  We take a look at random growth models through a central example known as the corner growth model. We describe some successes won over the last 30 years and some of the myriad challenges that remain. Specifically, we discuss limit shapes, scaling limits, the meaning of Kardar-Parisi-Zhang universality, and the global geometry of stochastic growth in terms of infinite geodesics and the stochastic counterpart of Busemann functions from metric geometry. This talk is aimed at a general math audience of graduate students and non-experts.