Karen Strung (Institute of Mathematics of the Czech Academy of Sciences) TBD Sponsored by the National Science Foundation
Thu, Mar. 26 3:35pm (MATH 3…
Probability
Andrew Campbell (ISTA)
X
A result dating back at least 40 years is that the roots of Hermite polynomials are asymptotically distributed according to the semicircle distribution, which is also serves the role of the normal distribution in Voiculescu's free probability theory. Hermite polynomials are also crucial to understanding the eigenvalues of the Gaussian Unitary Ensemble, a particularly important distribution of random matrices for which an infinite version is simple to define. We will discuss a class of polynomials which provide analogous approximations for other stable distributions in free probability and other infinite ensembles of random matrices. We will look at the asymptotic properties of the roots of these polynomials and how they arise naturally in the study of zeros of analytic functions. As a special case we will look at the corresponding polynomial for the Riemann zeta function. This talk is based mostly on joint work with Jonas Jalowy.
Polynomial approximations of free stable laws, infinite random matrices, and the Riemann zeta function.
Polynomial approximations of free stable laws, infinite random matrices, and the Riemann zeta function.