2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118069We 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 pagesComplex VariablesMathematical PhysicsProbability30B20; 30C15; 60G60; 82B10text