论文标题
高斯随机矩阵中高阶间距比的通用缩放
Universal scaling of higher-order spacing ratios in Gaussian random matrices
论文作者
论文摘要
使用类似Wigner的Momise对随机矩阵的高斯集合进行分析研究了高阶间距比。对于$ k $ -th的订单间距比（r^{（k）} $，$ k> 1）$ dimension $ 2K+1 $的矩阵。从较早的数值研究中知道的该比率的通用缩放关系在$ r^{（k）} \ rightArrow0 $和$ r^{（k）} \ rightArrow \ rightarrow \ infty $的渐近极限中得到了证明。
Higher-order spacing ratios are investigated analytically using a Wigner-like surmise for Gaussian ensembles of random matrices. For $k$-th order spacing ratio $(r^{(k)}$, $k>1)$ the matrix of dimension $2k+1$ is considered. A universal scaling relation for this ratio, known from earlier numerical studies, is proved in the asymptotic limits of $r^{(k)}\rightarrow0$ and $r^{(k)}\rightarrow \infty$.
