The hole probability for Gaussian random SU(2) polynomials

Abstract

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.

12 pages

References in corpus (1)

• Zeros of Random Analytic Functions