Spectral measure of large random Helson matrices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915814758678528 |
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| author | Qiu, Yanqi Zhen, Guocheng |
| author_facet | Qiu, Yanqi Zhen, Guocheng |
| contents | We study the limiting spectral measure of large random Helson matrices and large random matrices of certain patterned structures.
Given a real random variable $X \in L^{2+ \varepsilon}(\mathbb{P}) $ for some $\varepsilon > 0$ and $\mathrm{Var}(X) = 1$. For the random $n \times n$ Helson matrices generated by the independent copies of $X$, scaling the eigenvalues by $\sqrt{n}$, we prove the almost sure weak convergence of the spectral measure to the standard Wigner semi-circular law. Similar results are established for large random matrices with certain general patterned structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral measure of large random Helson matrices Qiu, Yanqi Zhen, Guocheng Probability Number Theory We study the limiting spectral measure of large random Helson matrices and large random matrices of certain patterned structures. Given a real random variable $X \in L^{2+ \varepsilon}(\mathbb{P}) $ for some $\varepsilon > 0$ and $\mathrm{Var}(X) = 1$. For the random $n \times n$ Helson matrices generated by the independent copies of $X$, scaling the eigenvalues by $\sqrt{n}$, we prove the almost sure weak convergence of the spectral measure to the standard Wigner semi-circular law. Similar results are established for large random matrices with certain general patterned structures. |
| title | Spectral measure of large random Helson matrices |
| topic | Probability Number Theory |
| url | https://arxiv.org/abs/2405.18796 |