The Hole Probability for Gaussian Entire Functions

Details The Hole Probability for Gaussian Entire Functions The Hole Probability for Gaussian Entire Functions

2009-09-07

arxiv.org/abs/0909.1270v3

Mathematics

Complex Variables

1 figure

Scientific paper

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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