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Critical values of Gaussian $ SU(2)$ random polynomials


Authors: Renjie Feng and Zhenan Wang
Journal: Proc. Amer. Math. Soc. 144 (2016), 487-502
MSC (2010): Primary 12E10
DOI: https://doi.org/10.1090/proc/12765
Published electronically: June 10, 2015
MathSciNet review: 3430828
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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\to \infty $.


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Additional Information

Renjie Feng
Affiliation: Department of Mathematics and Statistics, Mcgill University, Montreal, Quebec, Canada
Email: renjie@math.mcgill.ca

Zhenan Wang
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: zn_wang@math.northwestern.edu

DOI: https://doi.org/10.1090/proc/12765
Received by editor(s): July 26, 2014
Received by editor(s) in revised form: January 12, 2015
Published electronically: June 10, 2015
Communicated by: Walter Van Assche
Article copyright: © Copyright 2015 American Mathematical Society