A matrix model of a non-Hermitian $β$-ensemble
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912333169688576 |
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| author | Mezzadri, Francesco Taylor, Henry |
| author_facet | Mezzadri, Francesco Taylor, Henry |
| contents | We introduce the first random matrix model of a complex $β$-ensemble. The matrices are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite $β$-ensembles discovered by Dumitriu and Edelman (J. Math. Phys., Vol. 43, 5830 (2002)). The main feature of the model is that the exponent $β$ of the Vandermonde determinant in the joint probability density function (j.p.d.f.) of the eigenvalues can take any value in $\mathbb{R}_+$. However, when $β=2$, the j.p.d.f. does not reduce to that of the Ginibre ensemble, but it contains an extra factor expressed as a multidimensional integral over the space of the eigenvectors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_13184 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A matrix model of a non-Hermitian $β$-ensemble Mezzadri, Francesco Taylor, Henry Mathematical Physics Probability We introduce the first random matrix model of a complex $β$-ensemble. The matrices are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite $β$-ensembles discovered by Dumitriu and Edelman (J. Math. Phys., Vol. 43, 5830 (2002)). The main feature of the model is that the exponent $β$ of the Vandermonde determinant in the joint probability density function (j.p.d.f.) of the eigenvalues can take any value in $\mathbb{R}_+$. However, when $β=2$, the j.p.d.f. does not reduce to that of the Ginibre ensemble, but it contains an extra factor expressed as a multidimensional integral over the space of the eigenvectors. |
| title | A matrix model of a non-Hermitian $β$-ensemble |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2305.13184 |