The hole probability for Gaussian random SU(2) polynomials

Details The hole probability for Gaussian random SU(2) polynomials The hole probability for Gaussian random SU(2) polynomials

2006-10-23

arxiv.org/abs/math/0610686v1

Mathematics

Complex Variables

12 pages

Scientific paper

We 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.

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