Work

A matrix model of a non-Hermitian β-ensemble

Year: 2024

Type: article

Abstract: We introduce the first random matrix model of a complex [Formula: see text]-ensemble. The matrices are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite [Formula: see text]-ensembles discovered by [I. Dumitriu and A. Edelman, Matrix models for beta ensembles, J. Math. Phys. 43 (2002) 5830–5847]. The main feature of the model is that the exponent [Formula: see text] of the Vandermonde determinant in the joint probability density function (j.p.d.f.) of the eigenvalues can take any value in [Formula: see text] However, when [Formula: see text], 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.

Source: Random Matrices Theory and Application

DOI: 10.1142/s2010326324500278

Authors: Francesco Mezzadri, Henry Taylor

Institution: University of Bristol

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: DTP 2020-2021 University of Bristol, G6312446531