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

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 coefficie...

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Published in:Mathematics (Basel) 2023-10, Vol.11 (19), p.4061
Main Authors: Sheikh, Sajad A., Mir, Mohammad Ibrahim, Dar, Javid Gani, Almanjahie, Ibrahim M., Alshahrani, Fatimah
Format: Article
Language:English
Subjects:
Algebra
Coefficients
Distribution (Probability theory)
Eneström–Kakeya theorem
Normal distribution
Polynomials
random polynomials
Random variables
Schur stability
Statistical analysis
Theorems
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description 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.
doi_str_mv 10.3390/math11194061
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subjects Algebra
Coefficients
Distribution (Probability theory)
Eneström–Kakeya theorem
Normal distribution
Polynomials
random polynomials
Random variables
Schur stability
Statistical analysis
Theorems
title A Probabilistic Version of Eneström–Kakeya Theorem for Certain Random Polynomials
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