The complex zeros of random orthogonal polynomials
Probability
2022-01-10 v2 Classical Analysis and ODEs
Complex Variables
Statistics Theory
Statistics Theory
Abstract
We utilize Cauchy's argument principle in combination with the Jacobian of a holomorphic function in several complex variables and the first moment of a ratio of two correlated complex normal random variables to prove explicit formulas for the density and the mean distribution of complex zeros of random polynomials spanned by orthogonal polynomials on the unit circle and on the unit disk. We then inquire into the consequences of their asymptotical evaluations.
Cite
@article{arxiv.2108.09687,
title = {The complex zeros of random orthogonal polynomials},
author = {Christopher Corley and Andrew Ledoan and Aaron Yeager},
journal= {arXiv preprint arXiv:2108.09687},
year = {2022}
}
Comments
16 pages, 4 figures