## Probabilistic Operator Algebra Seminar: Conditionally free random variables: the two-states framework

Seminar | February 4 | 2-4 p.m. | 736 Evans Hall

Jorge Garza Vargas, UC Berkeley

Department of Mathematics

In non-commutative probability the notion of stochastic independence is not unique. Therefore an extension of free probability which produces a larger variety of limit laws is certainly of interest. In this seminar we will review the notion of conditional freeness, introduced by Bozejko and Speicher. We will survey some of the combinatorial and analytic tools that are used in this setting and obtain the corresponding limit theorems. For example, a central limit theorem will be deduced, with instances of the limiting distributions including the arcsine, semicircle and Bernoulli distributions and certain deformations of these.

dvv@math.berkeley.edu