BIMSA > Probability and Dynamical Systems Seminar Probability and Dynamical Systems Seminar Parreau Systems and Disjointness from Strong mixing
Parreau Systems and Disjointness from Strong mixing
Organizers
Yuval Peres , Shuo Qin
Speaker
Sohail Farhangi
Time
Tuesday, April 7, 2026 3:15 PM - 4:15 PM
Venue
A3-3-301
Online
Zoom 482 240 1589 (BIMSA)
Abstract
Many classical dichotomies in ergodic theory can be understood through the lens of disjointness, a notion introduced by Furstenberg in 1967. For example, every identity is disjoint from every ergodic system, every Kronecker system is disjoint from every weakly mixing system, and every zero entropy system is disjoint from every K-mixing system. Another well-studied class of systems in ergodic theory is strongly mixing systems, and in 2009, Parreau described a collection of systems that are disjoint from every strongly mixing system, which we call Parreau systems. We will define Parreau systems and discuss their disjointness properties. We will also mention how well-known classes of systems, such as Interval exchange transformations and substitution systems, are related to Parreau systems.