Combinatorics Seminar - Elliot Paquette

September 10, 2019
Thursday, September 12, 2019 - 10:20am
Math Tower 154
Combinatorics Seminar

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

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