Dynamics of Random Processes

June 10-14, 2019

The analysis of dynamical (or time-dependent) stochastic processes and their asymptotic behaviour is fundamental in both discrete and continuous probability. In some cases, the asymptotic behavior of the stochastic process exhibits interesting dynamics on its own. This can be seen, for example, in the context of front propagation arising asymptotically in branching Brownian motion. In other cases, interesting dynamical behaviour emerges from stochastic processes after rescaling. Examples include the study of rescaled random walks in random environments (which in some settings converge almost surely to a Brownian motion, and in others to jump processes), or the study of two-dimensional lattice models in statistical mechanics (many of which converge, provably or conjecturally, to Schramm-Loewner Evolutions). The goal of this program is to expose graduate and advanced undergraduate students to a variety of such topics of current interest within the study of dynamical stochastic processes.