论文标题
可计算的结构公式，用于分布$β$ -JACOBI EDGE特征值
Computable structural formulas for the distribution of the $β$-Jacobi edge eigenvalues
论文作者
论文摘要
雅各比集合是随机矩阵理论的经典合奏之一。应用中的突出是特征值在光谱边缘的特性，特别是最大的分布（例如，罗伊在多元统计中最大的根检验）和最小的（例如，线性系统的条件数量）特征值。我们确定了三个参数值的范围，这些参数值确定这些分布的差距概率是相对于特定碱基的有限总和，此外，还利用了Selberg积分理论基本的某个差分差异系统，以提供递归方案来计算相应的系数。
The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy's largest root test in multivariate statistics) and smallest (e.g.~condition numbers of linear systems) eigenvalues. We identify three ranges of parameter values for which the gap probability determining these distributions is a finite sum with respect to particular bases, and moreover make use of a certain differential-difference system fundamental in the theory of the Selberg integral to provide a recursive scheme to compute the corresponding coefficients.
