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.
| Comments: | 12 pages ,8 tables |
| Subjects: | Complex Variables (math.CV); Probability (math.PR) |
| MSC classes: | 26C10, 30C15, 60E15, 60E05, 62E17 |
| Cite as: | arXiv:2605.25017 [math.CV] |
| (or arXiv:2605.25017v1 [math.CV] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25017 arXiv-issued DOI via DataCite (pending registration) |
|
| Journal reference: | Journal of Applied Mathematics, Statistics and Informatics (JAMSI) ,JAMSI, 20 (2024), No. 1 |
From: Sajad Sheikh [view email]
[v1]
Sun, 24 May 2026 11:53:09 UTC (630 KB)
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