Precise asymptotics for the spectral radius of a large random matrix
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911787380637696 |
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| author | Cipolloni, Giorgio Erdős, László Xu, Yuanyuan |
| author_facet | Cipolloni, Giorgio Erdős, László Xu, Yuanyuan |
| contents | We consider the spectral radius of a large random matrix $X$ with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of $X$ in [29]. To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of $X-z$ for different complex shift parameters $z$ using the Dyson Brownian Motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15643 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Precise asymptotics for the spectral radius of a large random matrix Cipolloni, Giorgio Erdős, László Xu, Yuanyuan Probability 15B52, 60B20 We consider the spectral radius of a large random matrix $X$ with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of $X$ in [29]. To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of $X-z$ for different complex shift parameters $z$ using the Dyson Brownian Motion. |
| title | Precise asymptotics for the spectral radius of a large random matrix |
| topic | Probability 15B52, 60B20 |
| url | https://arxiv.org/abs/2210.15643 |