<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Probabilistic zero bounds of certain random polynomials

Journal of Applied Mathematics, Statistics and Informatics

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Probabilistic zero bounds of certain random polynomials"}

This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random...

Probabilistic zero bounds of certain random polynomials

Published Online: Jun 03, 2024

Page range: 53 - 66

DOI: https://doi.org/10.2478/jamsi-2024-0004

Keywords
Random polynomials, Probability density function, Normal random variable, Cauchy distribution, Probabilistic bounds, Error function

© 2024 S. A. Sheikh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Probabilistic zero bounds of certain random polynomials

Published Online: Jun 03, 2024

Page range: 53 - 66

DOI: https://doi.org/10.2478/jamsi-2024-0004

KeywordsRandom polynomials, Probability density function, Normal random variable, Cauchy distribution, Probabilistic bounds, Error function

© 2024 S. A. Sheikh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Random polynomials, Probability density function, Normal random variable, Cauchy distribution, Probabilistic bounds, Error function