arXiv math/03122582003-12-12math.CVmath-phmath.MPmath.PR

Random complex zeroes, III. Decay of the hole probability

Mikhail Sodin, Boris Tsirelson

备注：: 10 pages
发表信息：: Israel Journal of Mathematics 147 (2005), 371--379.

英文摘要：

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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