论文标题
各种pólya集合的正定矩阵的融合速率
Rate of convergence at the hard edge for various Pólya ensembles of positive definite matrices
论文作者
论文摘要
正定随机矩阵的pólya集合的理论为相应的生物表决对提供了结构公式和相关核，它们非常适合计算硬边缘大$ n $渐近学。进行了这种分析，针对Laguerre合奏，Laguerre Muttalib-Borodin集团以及Laguerre合奏及其倒置的产物进行了这种分析。后者包括雅各比统一合奏的特殊情况。在每种情况下，硬边缩放的内核都允许以$ 1/n $的功率扩展，并以结构化形式给出的领先术语涉及生物表现对的硬边缩放。 Laguerre和Jacobi合奏具有特殊功能，即它们的硬边缩放内核（Bessel内核）是对称的，这导致有选择的硬边缩放变量选择，相关功能的收敛速率为$ O（1/N^2）$。
The theory of Pólya ensembles of positive definite random matrices provides structural formulas for the corresponding biorthogonal pair, and correlation kernel, which are well suited to computing the hard edge large $N$ asymptotics. Such an analysis is carried out for products of Laguerre ensembles, the Laguerre Muttalib-Borodin ensemble, and products of Laguerre ensembles and their inverses. The latter includes as a special case the Jacobi unitary ensemble. In each case the hard edge scaled kernel permits an expansion in powers of $1/N$, with the leading term given in a structured form involving the hard edge scaling of the biorthogonal pair. The Laguerre and Jacobi ensembles have the special feature that their hard edge scaled kernel -- the Bessel kernel -- is symmetric and this leads to there being a choice of hard edge scaling variables for which the rate of convergence of the correlation functions is $O(1/N^2)$.
