Fluctuations in the zero set of the hyperbolic Gaussian analytic function
Complex Variables
2016-02-10 v1 Probability
Abstract
The zero set of the hyperbolic Gaussian analytic function is a random point process in the unit disc whose distribution is invariant under automorphisms of the disc. We study the variance of the number of points in a disc of increasing radius. Somewhat surprisingly, we find a change of behaviour at a certain value of the `intensity' of the process, which appears to be novel.
Keywords
Cite
@article{arxiv.1307.6674,
title = {Fluctuations in the zero set of the hyperbolic Gaussian analytic function},
author = {Jeremiah Buckley},
journal= {arXiv preprint arXiv:1307.6674},
year = {2016}
}
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18 pages