Exploring continuous beta-ensembles: A Python implementation for random matrix spectral statistics

Abstract

We present an open-source Python package for sampling the Gaussian, Laguerre, Jacobi, and Circular $\beta$-ensembles of random matrix theory. The package implements the Dumitriu--Edelman and Killip--Nenciu constructions, allowing efficient generation of random spectra for general $\beta >0$. In addition to spectrum generation, it includes tools for the analysis of spectral statistics, from standard nearest-neighbor spacings and spacing ratios to non-adjacent $k$-spacings and the spectral form factor. These tools can be applied to generic spectral data, allowing users to compare them with and fit them to $\beta$-ensemble predictions. In this note, we review the $\beta$-ensembles, describe the package interface, and illustrate its use through several numerical experiments motivated by applications to quantum chaos. Our numerical results include an analysis of $\beta$ as a continuous fitting parameter in spacing ratio statistics, an examination of the numerical evidence for the conjectured $k$-spacing ratio distributions, and a study of the spectral form factor for general values of $\beta$.

arXiv commentv2: updated to add Jacobi ensembles and document other new features of the package. results unchanged