Random complex zeroes, III. Decay of the hole probability
Complex Variables
2007-05-23 v1 Mathematical Physics
math.MP
Probability
Abstract
By a hole we mean a disc that contains no flat chaotic analytic zero points (i.e. zeroes of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!). A given disc of radius r has a probability of being a hole, - the hole probability. We show that for large r the hole probability decays as exp(-cr^4).
Cite
@article{arxiv.math/0312258,
title = {Random complex zeroes, III. Decay of the hole probability},
author = {Mikhail Sodin and Boris Tsirelson},
journal= {arXiv preprint arXiv:math/0312258},
year = {2007}
}
Comments
10 pages