Analysis Seminar: Random Commuting Matrices

Speaker: John McCarthy, Washington University in St. Louis

Abstract: The study of the eigenvalue distribution of random matrices is a well-established field, dating back to the 1920's. It became popular with the work of Wigner and Dyson in the 1950's and 60's, and today is a major field in both probability and theoretical physics. What can one say about random d-tuples of commuting matrices? What does it even mean? We will describe one possible approach to defining a random d-tuple of commuting matrices. We shall show that in the Hermitian case, the description of their eigenvalue distribution parallels to some extent the single matrix theory, but in the non-self adjoint case it does not.