Critical values of Gaussian 𝑆𝑈(2) random polynomials

Feng, Renjie; Wang, Zhenan

doi:10.1090/proc/12765

Critical values of Gaussian $SU(2)$ random polynomials
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by Renjie Feng and Zhenan Wang

Proc. Amer. Math. Soc. 144 (2016), 487-502

DOI: https://doi.org/10.1090/proc/12765

Published electronically: June 10, 2015

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Abstract:

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

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