Conditional Measures for the Zero Set of the Gaussian Analytic Function
Channel: ICTP Mathematics
Date: 2021-09-20

Speaker: Alexander BUFETOV, Aix-Marseille University

Abstract: Consider a random series whose entries are independent complex Gaussians with expectation zero and variance 1. The radius of convergence of this series is 1. The Peres-Viràg theorem gives an explicit determinantal formula for the correlation functions of the zero set; it turns out, in particular, that if the unit disc is considered as the Poincaré model for the Lobachevsky plane, then the distribution of the zero set is invariant under Lobachevskian isometries. The main result of the talk is an explicit descriptiopn of conditional distributions of the zero set subject to the condition that the configuration is fixed in the complement of a compact set.