Random complex zeroes, III. Decay of the hole probability

Details Random complex zeroes, III. Decay of the hole probability Random complex zeroes, III. Decay of the hole probability

2003-12-12

arxiv.org/abs/math/0312258v1

Israel Journal of Mathematics 147 (2005), 371--379.

Mathematics

Complex Variables

10 pages

Scientific paper

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).

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