Free Probability Seminar

Date: February 18, 2016

Time: 2:30PM - 3:30PM

Location: BLOC 605AX

Speaker: Ken Dykema, TAMU

Title: On algebra-valued R-diagonal elements

Abstract: R-diagonal elements in usual, scalar-valued *-noncommutative probability spaces include some of the non-self-adjoint operators that have been among those most studied in free probability theory. Analogous elements in the algebra-valued setting (also called operator-valued or amalgamated setting) were introduced by Sniady and Speicher in 2001, but have not been much investigated since then. A case of them arose naturally in studies of certain random Vandermonde matrices. In this talk, we describe characterizations of algebra-valued R-diagonal elements. One of these is in terms of non-crossing cumulants. We will also describe some results and examples concerning *-freeness of the unitary part and absolute values arising in the polar decompositions of some algebra-valued R-diagonal elements and algebra-valued circular elements. (Joint work with March Boedihardjo.)