The complex zeros of random orthogonal polynomials

Autor:	Corley, Christopher, Ledoan, Andrew, Yeager, Aaron
Rok vydání:	2021
Předmět:	Mathematics - Probability Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables Mathematics - Statistics Theory 30C15 30C10 30C40 30E15 32A10 32A25 42C05
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2108.09687 Zobrazit plný text záznamu View this record from Arxiv