A matrix model of a non-Hermitian β -ensemble

Francesco Mezzadri*, Henry Taylor

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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 languageEnglish
Article number2450027
JournalRandom Matrices: Theory and Applications
Early online date13 Jan 2025
DOIs
Publication statusE-pub ahead of print - 13 Jan 2025

Bibliographical note

Publisher Copyright:
© 2024 World Scientific Publishing Company.

Fingerprint

Dive into the research topics of 'A matrix model of a non-Hermitian β -ensemble'. Together they form a unique fingerprint.

Cite this