Nearest zero-critical point distances for Gaussian SU(2) polynomials

Renjie Feng

paper

Nearest zero-critical point distances for Gaussian SU(2) polynomials

arXiv:2606.09712

Abstract

We study nearest zero--critical point distances for the Gaussian SU(2) polynomial $p_{n}$ . For each zero $z_{i}$ of $p_{n}$ , let $D_{n} (z_{i})$ denote its Fubini--Study distance to the nearest critical point. We prove that the empirical measure of the rescaled distances $n D_{n} (z_{i})$ converges weakly in probability to the law of $2/∣ Z ∣$ , where $Z$ is distributed according to the Fubini--Study probability measure in the affine chart.