The Hole Probability for Gaussian Entire Functions
Complex Variables
2010-04-07 v3 Probability
Abstract
We study the hole probability of Gaussian random entire functions. More specifically, we work with entire functions in Taylor series form with i.i.d complex Gaussian coefficients. A hole is the event where the function has no zeros in a disc of radius r. We find exact asymptotics for the rate of decay of the hole probability for large values of r, outside a small exceptional set (which is deterministic).
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Cite
@article{arxiv.0909.1270,
title = {The Hole Probability for Gaussian Entire Functions},
author = {Alon Nishry},
journal= {arXiv preprint arXiv:0909.1270},
year = {2010}
}
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