Title: The Gaussian analytic function is either bounded or covers the plane
Speaker: Elliot Paquette, OSU
Abstract: The Gaussian analytic function (GAF) is a power series with independent Gaussian coefficients. In the case that this power series has radius of convergence 1, it is a classical theorem that the power series is a.s. bounded on the open disk if and only if it extends continuously to a function on the closed unit disk a.s. Nonetheless, there exists a natural range of coefficients in which the GAF has boundary values in L-p, but is a.s. unbounded. How wild are these boundary values? Well, Kahane asked if a GAF either a.s. extends continuously to the closed disk or a.s. has range covering the whole plane. We discuss this and other problems and introduce a useful heuristic for understanding these problems in terms of branching processes.
Joint with Alon Nishry.
Seminar URL: u.osu.edu/probability
