Universal scaling of higher-order spacing ratios in Gaussian random matrices
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Universal scaling of higher-order spacing ratios in Gaussian random matrices
Udaysinh T. Bhosale
AbstractHigher-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 $r^{(k)}\rightarrow \infty$.