Probabilistic Operator Algebra Seminar: On convolutions and transforms in operator valued free probability

Seminar | October 23 | 3:45-5:45 p.m. | 748 Evans Hall

 Weihua Liu, Indiana University

 Department of Mathematics

In this talk, I will introduce a class of independence relations which include free, Boolean and monotone independence in operator valued probability. I will briefly review some analytic properties of operator-valued free, Boolean and monotone convolutions. After that, I will show some analytic properties of two other important convolutions which are called orthogonal convolution and s-free convolution ( or say subordination convolution). We will see that most convolutions in our framework can be constructed from the orthogonal and the Boolean convolution whereas the s-free convolution is a powerful tool for studying the free additive convolution. Then I will show how to use matricial functions which are derived from Voiculescu's fully matricial function theory, to study relations between convolutions and transforms in operator-valued free probability. If time permits, I will simply explain how to compute large N laws of random matrices with entries of our new independent relations, and we will see that the large N laws are not always semicircular.