تقرير
A matrix model of a non-Hermitian $\beta$-ensemble
| العنوان: | A matrix model of a non-Hermitian $\beta$-ensemble |
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| المؤلفون: | Mezzadri, Francesco, Taylor, Henry |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Mathematics - Probability |
| الوصف: | We introduce the first random matrix model of a complex $\beta$-ensemble. The matrices are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite $\beta$-ensembles discovered by Dumitriu and Edelman (J. Math. Phys., Vol. 43, 5830 (2002)). The main feature of the model is that the exponent $\beta$ 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 $\beta=2$, 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. Comment: 23 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.13184 |
| رقم الأكسشن: | edsarx.2305.13184 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |