Phase transitions on one-dimensional symbolic systems
By Tamara Kucherenko
By Bryna Kra
Appears in collections : Probabilistic aspects of multiple ergodic averages / Aspects probabilistes des moyennes ergodiques multiples, Exposés de recherche
The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on convergence results and what can be said about the limits.