1 Overview of the fleld Our research project is in the area of noncommutative probability. Noncommutative probability emerged in the early ’80s as a very powerful tool for the study of flnite… Expand

In his article On the free convolution with a semicircular distribution, Biane found very useful characterizations of the boundary values of the imaginary part of the Cauchy–Stieltjes transform of… Expand

Author(s): Curran, Stephen Robert | Advisor(s): Voiculescu, Dan-Virgil | Abstract: The framework of this thesis is Voiculescu's free probability theory. The main theme is the application of… Expand

We consider the framework of an operator-valued noncommutative probability space over a unital C*-algebra B. We show how for a B-valued distribution \mu one can define convolution powers with respect… Expand