Speaker: Ken Dykema
Affiliation: Texas A&M University,
Title:
Multilinear function series and transforms in free probability theory
Time and Place: Mondays, 1/23 and 1/30, 3:00-3:55pm, Milner 317.
Abstract: The R- and S-transforms are used in free probability theory to find the generating functions of the sum and product, respectively, of free random variables. After describing these in the case of a scalar-valued noncommutative probability space, we will consider the case of a B--valued noncommutative probability space for B a Banach algebra, and we will prove the desired properties of the R- and S-transforms in this case. We will then turn to an algebraic formulation that is possible using the formalism of multilinear function series. This allows treatment of unsymmetrized moments, via the so-called unsymmetrized R- and S-transforms. Some interesting combinatorics arising from this approach will also be described.