The order of the decay of the hole probability for Gaussian random SU(m+1) polynomials

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dc.creatorZrebiec, Scott
dc.date2007-04-20
dc.date.accessioned2026-07-07T07:57:37Z
dc.date.available2026-07-07T07:57:37Z
dc.descriptionWe show that for Gaussian random SU(m+1) polynomials of a large degree N the probability that there are no zeros in the disk of radius r is less than $e^{-c_{1,r} N^{m+1}}$, and is also greater than $e^{-c_{2,r} N^{m+1}}$. Enroute to this result, we also derive a more general result: probability estimates for the event where the volume of the zero set of a random polynomial of high degree deviates significantly from its mean.
dc.descriptionThis paper generalizes one which was previously posted by the author
dc.identifierhttps://arxiv.org/abs/0704.2733
dc.identifierhttp://arxiv.org/abs/0704.2733
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127712
dc.subjectComplex Variables
dc.subjectProbability
dc.subject30B20; 30C15; 60G60; 82B10
dc.titleThe order of the decay of the hole probability for Gaussian random SU(m+1) polynomials
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