Probabilistic zero bounds of certain random polynomials-Reference-Cited by-同舟云学术

Probabilistic zero bounds of certain random polynomials

Published:2024-05-01 Issue:1 Volume:20 Page:53-66
ISSN:1339-0015
Container-title:Journal of Applied Mathematics, Statistics and Informatics
language:en
Short-container-title:

Author:

Sheikh S. A.¹,Mir M. I.¹

Affiliation:

1. Department of Mathematics , University of Kashmir , South Campus, Anantnag 192101, Jammu and Kashmir , India

Abstract

Abstract This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coefficients are independently and identically distributed as standard normal variates. Additionally, the paper provides a clear exposition of the developed methodology. To establish our results, we develop a novel approach utilizing the classical Cauchy’s bounds for the zeros of a deterministic polynomial with complex coefficients. We also corroborate our analytical results with extensive simulations. The methodology developed in the paper can potentially be applied to a broad class of problems regarding bounds and the distribution of zeros in the theory of random polynomials.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/jamsi-2024-0004

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