Zeroes of Gaussian analytic functions

Details Zeroes of Gaussian analytic functions Zeroes of Gaussian analytic functions

2004-10-14

arxiv.org/abs/math/0410343v1

Mathematics

Complex Variables

Talk at the 4th European Congress of Mathematics (Stockholm, 2004)

Scientific paper

Geometrically, zeroes of a Gaussian analytic function are intersection points of an analytic curve in a Hilbert space with a randomly chosen hyperplane. Mathematical physics provides another interpretation as a gas of interacting particles. In the last decade, these interpretations influenced progress in understanding statistical patterns in the zeroes of Gaussian analytic functions, and led to the discovery of canonical models with invariant zero distribution. We shall discuss some of recent results in this area and mention several open questions.

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