Free probability inequalities on the circle and a conjecture

Analysis Seminar
Wednesday, September 5, 2018 - 1:55pm for 1 hour (actually 50 minutes)
Skiles 006
Ionel Popescu – Georgia Institute of Technology
Galyna Livshyts
I will discuss some free probability inequalities on the circle which can be seen in two different ways, one is via random matrix approximation, and another one by itself. I will show what I believe to be the key of these new forms, namely the fact that the circle acts on itself. For instance the Poincare inequality has a certain form which reflects this aspect. I will also briefly show how a transportation inequality can be discussed and how the standard Wasserstein distance can be modified to introduce this interesting phenomena. I will end the talk with a conjecture and some supporting evidence in the classical world of functional inequalities.