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

Sajad A. Sheikh, Mohammad Ibrahim Mir, Javid Gani Dar (), Ibrahim M. Almanjahie and Fatimah Alshahrani
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Sajad A. Sheikh: Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, India
Mohammad Ibrahim Mir: Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, India
Javid Gani Dar: Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune 412115, India
Ibrahim M. Almanjahie: Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia
Fatimah Alshahrani: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Mathematics, 2023, vol. 11, issue 19, 1-11

Abstract: 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.

Keywords: Eneström–Kakeya theorem; random polynomials; normal distribution; Schur stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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