Abstract
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., 43 (2002), 5830. 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 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.
Original language | English |
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Article number | 2450027 |
Journal | Random Matrices: Theory and Applications |
Early online date | 13 Jan 2025 |
DOIs | |
Publication status | E-pub ahead of print - 13 Jan 2025 |
Bibliographical note
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