Dynamical Systems Seminar
Friday March 9th, 2018
Time: 2:30 PM - 3:30 PM
Title: Stochastic homogenization and dynamics
Speaker: Vadim Kaimanovich, University of Ottawa
Location: Math Tower P-131
The key point of Shannon's information theory consists in passing from finite strings of symbols to infinite ones with a subsequent study of shift-invariant measures on infinite words. One can extend this idea from strings of symbols (i.e., linear graphs) to general finite graphs. In this case the role of the space of infinite words is played by the space of locally finite infinite rooted graphs. This space is endowed with a natural root moving equivalence relation, so that one can talk about the measures invariant with respect to this relation. Random graphs sampled from an invariant measure are called stochastically homogeneous. Similar notions of unimodular random graphs and invariant random subgroup are currently quite popular in probability and group theory. In this talk (partially based on joint work with Paul-Henry Leemann and Tatiana Nagnibeda) I will discuss a new example of stochastic homogenization arising from the homoclinic equivalence relations of symbolic dynamical systems.