Asymptotics of The Hole Probability for Zeros of Random Entire Functions
Complex Variables
2016-09-20 v2 Probability
Abstract
We study the hole probability of Gaussian random entire functions. More specifically, we work with the flat model (the zero set of this function has a distribution which is invariant with respect to the plane isometries). A hole is the event where the function has no zeros in a disc of radius r. We show that the logarithm of the probability of the hole event decays asymptotically like -1/4 * e^2 * r^4 + o(r^4). We also study the behavior of the hole probability with other types of random coefficients.
Cite
@article{arxiv.0903.4970,
title = {Asymptotics of The Hole Probability for Zeros of Random Entire Functions},
author = {Alon Nishry},
journal= {arXiv preprint arXiv:0903.4970},
year = {2016}
}
Comments
21 pages