Random complex zeroes, III. Decay of the hole probability

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dc.creatorSodin, Mikhail
dc.creatorTsirelson, Boris
dc.date2003-12-12
dc.date.accessioned2026-07-07T06:21:35Z
dc.date.available2026-07-07T06:21:35Z
dc.descriptionBy 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).
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0312258
dc.identifierhttp://arxiv.org/abs/math/0312258
dc.identifierIsrael Journal of Mathematics 147 (2005), 371--379.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95644
dc.subjectComplex Variables
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject30B20; 30C15, 60G60, 82B10
dc.titleRandom complex zeroes, III. Decay of the hole probability
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