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arXiv · 1307.6674

Fluctuations in the zero set of the hyperbolic Gaussian analytic function

Jeremiah Buckley
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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.

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Jeremiah Buckley. 2013-07-25. Fluctuations in the zero set of the hyperbolic Gaussian analytic function. https://doi.org/10.1093/imrn%2Frnt269

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