Conditional Measures for the Zero Set of the Gaussian Analytic Function

Explore the intricacies of conditional measures for the zero set of the Gaussian Analytic Function in this one-hour lecture by Alexander Bufetov from Aix-Marseille University. Delve into the properties of random series with independent complex Gaussian entries, focusing on their behavior within the unit disc. Examine the Peres-Viràg theorem and its implications for the correlation functions of the zero set, including the invariance under Lobachevskian isometries when considering the unit disc as the Poincaré model for the Lobachevsky plane. Discover the main result of the talk, which provides an explicit description of conditional distributions of the zero set when the configuration is fixed in the complement of a compact set. Gain insights into advanced mathematical concepts at the intersection of complex analysis, probability theory, and geometry.