Title: Large fluctuations in the number of zeros for Gaussian Taylor series
Speaker: Alon Nishry
Speaker Info: Univ. of Michigan
Brief Description:
Special Note:
Abstract:
We study two types of random Taylor series with independent complex Gaussian coefficients. These Taylor series are distinguished by the invariance of their zero sets with respect to isometries of the complex plane (’flat’ model) or the unit disk (‘hyperbolic’). In the flat case, we consider the very rare event where the number of zeros in a large disk is far from the expected value. We are interested in the probability of this event, and also in the conditional distribution of the zeros, given this event. For the hyperbolic model, we focus on the ‘hole’ event - when there are no zeros in a disk centered at the origin. We find asymptotic bounds for the logarithm of the probability of this event, as the radius of the disk goes to 1.Date: Saturday, April 02, 2016