Free Probability and Operators

Date: February 17, 2023

Time: 4:00PM - 5:00PM

Location: BLOC 306

Speaker: Michael Anshelevich, TAMU

Title: Hermite trace polynomials

Abstract: We consider the algebra of trace polynomials with the state induced by the GUE random matrices. In addition to the monomial basis, another natural basis for this algebra consists of the Hermite trace polynomials. They satisfy several properties familiar for the ordinary trace polynomials. The algebra structure can be extended from polynomials to a larger family of stochastic integrals. While the Hermite trace polynomials are not orthogonal, they can be modified to obtain several versions of the chaos decomposition. The simplest of these is related to the Hermite polynomials of matrix argument. This is joint work with David Buzinski.