Probabilistic Zero Bounds of Certain Random Polynomials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914601786933248 |
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| author | Sheikh, Sajad A. Mir, Mohammad Ibrahim |
| author_facet | Sheikh, Sajad A. Mir, Mohammad Ibrahim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25017 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Probabilistic Zero Bounds of Certain Random Polynomials Sheikh, Sajad A. Mir, Mohammad Ibrahim Complex Variables Probability 26C10, 30C15, 60E15, 60E05, 62E17 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. |
| title | Probabilistic Zero Bounds of Certain Random Polynomials |
| topic | Complex Variables Probability 26C10, 30C15, 60E15, 60E05, 62E17 |
| url | https://arxiv.org/abs/2605.25017 |