Roland Speicher, Universität des Saarlandes

Abstract: Free probabiility theory was invented by Dan Voiculescu as a non-commutative analogue of classical probability theory, in order to understand the structure of specific non-commutative operator algebras from a kind of non-commutative probabilistic perspective. Later, Voiculescu discovered that free probability also describes the large N asymptotics of many random matrices. As large random matrices are becoming more and more prominent in many different subjects (like wireless communications, financial mathematics, machine learning, quantum information) free probability has since its beginnings reached out to many different communities. 

I will give in my talks an introduction to free probability, as well as a flavor of its quite developed analytical, combinatorial, and probabilistic theory, in particular also pointing out the similarities and differences to classical probability theory.