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 β-ensembles of random matrix theory. The package implements the Dumitriu--Edelman and Killip--Nenciu constructions, allowing efficient generation of random spectra for general β> 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 β-ensemble predictions. In this note, we review the β-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 β 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 β.
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BibTeX
@misc{weissman2026exploring,
title = {{Exploring continuous beta-ensembles: A Python implementation for random matrix spectral statistics}},
author = {Dorin Weissman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.27224},
eprint = {2608.27224},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27224},
}
RIS
TY - UNPB
TI - Exploring continuous beta-ensembles: A Python implementation for random matrix spectral statistics
AU - Dorin Weissman
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2608.27224
UR - https://arxiv.org/abs/2608.27224
AB - We present an open-source Python package for sampling the Gaussian, Laguerre, Jacobi, and Circular β-ensembles of random matrix theory. The package implements the Dumitriu--Edelman and Killip--Nenciu constructions, allowing efficient generation of random spectra for general β> 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 β-ensemble predictions. In this note, we review the β-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 β 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 β.
ER -