A Probabilistic Version of Eneström–Kakeya Theorem for Certain Random Polynomials

Autor:	Sajad A. Sheikh, Mohammad Ibrahim Mir, Javid Gani Dar, Ibrahim M. Almanjahie, Fatimah Alshahrani
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Eneström–Kakeya theorem random polynomials normal distribution Schur stability Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 19, p 4061 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11194061
Popis:	This paper presents a comprehensive exploration of a probabilistic adaptation of the Eneström–Kakeya theorem, applied to random polynomials featuring various coefficient distributions. Unlike the deterministic rendition of the theorem, our study dispenses with the necessity of any specific coefficient order. Instead, we consider coefficients drawn from a spectrum of sets with diverse probability distributions, encompassing finite, countable, and uncountable sets. Furthermore, we provide a result concerning the probability of failure of Schur stability for a random polynomial with coefficients distributed independently and identically as standard normal variates. We also provide simulations to corroborate our results.
Databáze:	Directory of Open Access Journals
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