Critical values of Gaussian SU(2) random polynomials

Abstract

In this note, we will get the estimate of the expected distribution of critical values of Gaussian SU(2) random polynomials as the degree large enough. The result is a direct application of the Kac-Rice formula. The critical values will accumulate at infinity, we further study the rate of this convergence and its rescaling limit as $n\to \infty$.

the growth of critical values is further studied, the rescaling limit of the density is added, some typos are fixed, to appear in Proceeding of AMS

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