Random Power Series

Abstract: The aim of the talk is to discuss the main properties of random complex valued power series whose coefficients are in a sequence of random variables. Assuming independence of the coefficients and few more conditions, we will see that the random holomorphic function obtained has a natural boundary at the circle of convergence almost surely. Time permitting, we will also see that, under very similar hypothesis, the zeros of the sections of a random power series are almost surely asymptotically equidistributed on the circle of convergence.

Host: Christopher Felder