Concentration inequalities for the number of real zeros of Kac polynomials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911749243928576 |
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| author | Can, Van Hao Nguyen, Oanh |
| author_facet | Can, Van Hao Nguyen, Oanh |
| contents | We study concentration inequalities for the number of real roots of the classical Kac polynomials $$f_{n} (x) = \sum_{i=0}^n ξ_i x^i$$ where $ξ_i$ are independent random variables with mean 0, variance 1, and uniformly bounded $(2+\ep_0)$-moments. We establish polynomial tail bounds, which are optimal, for the bulk of roots. For the whole real line, we establish sub-optimal tail bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15446 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Concentration inequalities for the number of real zeros of Kac polynomials Can, Van Hao Nguyen, Oanh Probability We study concentration inequalities for the number of real roots of the classical Kac polynomials $$f_{n} (x) = \sum_{i=0}^n ξ_i x^i$$ where $ξ_i$ are independent random variables with mean 0, variance 1, and uniformly bounded $(2+\ep_0)$-moments. We establish polynomial tail bounds, which are optimal, for the bulk of roots. For the whole real line, we establish sub-optimal tail bounds. |
| title | Concentration inequalities for the number of real zeros of Kac polynomials |
| topic | Probability |
| url | https://arxiv.org/abs/2311.15446 |