arXiv math/06106862006-10-23math.CVmath-phmath.MPmath.PR

The hole probability for Gaussian random SU(2) polynomials

Scott Zrebiec

备注：: 12 pages

英文摘要：

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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