1er juillet 2019

Vadim Kaimanovich (Université d'Ottawa)
Stochastic homogenization and dynamics

Plus d'infos...

Lieu : salle 3L15

Résumé : 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 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 works with Paul-Henry Leemann, Tatiana Nagnibeda and Blair Drummond) I will discuss new examples of stochastic homogenization arising from the homoclinic equivalence relations of symbolic dynamical systems. More specifically, I will describe the relationship of the limit measures on the space of graphs arising from the de Bruijn (or, Rauzy) graphs of subshifts of finite type and of low complexity subshifts with the corresponding shift-invariant measures.

Stochastic homogenization and dynamics  Version PDF