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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Sajad A. Sheikh & Mohammad Ibrahim Mir & Javid Gani Dar & Ibrahim M. Almanjahie & Fatimah Alshahrani, 2023. "A Probabilistic Version of Eneström–Kakeya Theorem for Certain Random Polynomials," Mathematics, MDPI, vol. 11(19), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4061-:d:1247164
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