Title: Relative Asymptotics of Orthogonal Polynomials
Speaker: Brian Simanek (Baylor University)
Abstract: We will explore the relationship between the asymptotic behavior of orthogonal polynomials and the entries of the Bergman Shift matrix. In particular, we will show that certain asymptotic behaviors such as ratio asymptotics can be related to the behavior of these matrix entries as we move along the diagonals. This will allow us to show that relative ratio asymptotic behavior occurs in some surprising examples. As an application, we will explore consequences of this result in the setting of random orthogonal polynomials on the unit circle or real line.