探索连续β系综：用于随机矩阵谱统计的Python实现
Exploring continuous beta-ensembles: A Python implementation for random matrix spectral statistics
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- INFN Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）
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中文总结 AI 辅助
该研究开发了用于采样随机矩阵理论中β系综的开源Python包，实现了相关构造，提供谱统计分析工具，并通过数值实验验证了β作为连续拟合参数等内容。
中文摘要 AI 辅助
我们提出一个开源Python包，用于采样随机矩阵理论中的高斯、圆和拉盖尔β系综。该包实现了Dumitriu-Edelman和Killip-Nenciu构造，可高效生成β>0时的随机谱。除谱生成外，它还包含谱统计分析工具，涵盖标准最近邻间距、间距比，以及非相邻k间距和谱形状因子。这些工具可应用于通用谱数据，让用户将其与β系综预测结果进行比较和拟合。在本注中，我们回顾β系综，描述包的接口，并通过受量子混沌应用启发的多个数值实验说明其使用方法。我们的数值结果包括对间距比统计中β作为连续拟合参数的分析、对猜想k间距比分布的数值证据的检验，以及对一般β值下谱形状因子的研究。
英文摘要
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 $β$.
