Probabilistic Operator Algebra Seminar: Free probability and polynomial convolutions: the tropical case.

Seminar | November 27 | 3:45-5:45 p.m. | 748 Evans Hall

 Jorge Garza Vargas, UC Berkeley

 Department of Mathematics

This talk will be divided in two parts. First we will explore two polynomial convolutions that stem from the work of Marcus, Spielman and Srivastava on interlacing families of polynomials. As noted by Marcus, in the limit these convolutions converge to the respective free convolution. We will briefly discuss this phenomenon and provide a sketch of the machinery constructed by Marcus to deal with the theory that arises from this observation (finite-free probability). Second, we will focus in the framework of idempotent mathematics ( also known as tropical mathematics). By using Maslov's dequantization, we will find the analogs of finite-free convolutions in the idempotent setting and review the results of Rosenmann, Lehner and Peperko on these convolutions. Finally we will conclude by pointing out the relations between these convolutions and the max-free convolution of Ben Arous and Voiculescu.