Roots of random trigonometric polynomials with general dependent coefficients
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914955230445568 |
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| author | Angst, Jürgen Nguyen, Oanh Poly, Guillaume |
| author_facet | Angst, Jürgen Nguyen, Oanh Poly, Guillaume |
| contents | We consider random trigonometric polynomials with general dependent coefficients. We show that under mild hypotheses on the structure of dependence, the asymptotics as the degree goes to infinity of the expected number of real zeros coincides with the independent case. To the best of our knowledge, this universality result is the first obtained in a non-Gaussian dependent context. Our proof highlights the robustness of real zeros, even in the presence of dependencies. These findings bring the behavior of random polynomials closer to real-world models, where dependencies between coefficients are common. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Roots of random trigonometric polynomials with general dependent coefficients Angst, Jürgen Nguyen, Oanh Poly, Guillaume Probability 26C10 We consider random trigonometric polynomials with general dependent coefficients. We show that under mild hypotheses on the structure of dependence, the asymptotics as the degree goes to infinity of the expected number of real zeros coincides with the independent case. To the best of our knowledge, this universality result is the first obtained in a non-Gaussian dependent context. Our proof highlights the robustness of real zeros, even in the presence of dependencies. These findings bring the behavior of random polynomials closer to real-world models, where dependencies between coefficients are common. |
| title | Roots of random trigonometric polynomials with general dependent coefficients |
| topic | Probability 26C10 |
| url | https://arxiv.org/abs/2409.15057 |