The hole probability for Gaussian random SU(2) polynomials

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dc.creatorZrebiec, Scott
dc.date2006-10-23
dc.date.accessioned2026-07-07T07:29:20Z
dc.date.available2026-07-07T07:29:20Z
dc.descriptionWe show that for Gaussian random SU(2)polynomials of a large degree $N$ the probability that there are no zeros in the disk of radius $r$ is less than $e^{-c_{1,r} N^2}$, and is also greater than $e^{-c_{2,r} N^2}$. Enroute to this result, we also derive a more general result: probability estimates for the event that the number of complex zeros of a random polynomial of high degree deviates significantly from its mean.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0610686
dc.identifierhttp://arxiv.org/abs/math/0610686
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118069
dc.subjectComplex Variables
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject30B20; 30C15; 60G60; 82B10
dc.titleThe hole probability for Gaussian random SU(2) polynomials
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