Universal scaling of higher-order spacing ratios in Gaussian random matrices

Abstract

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 $r^{(k)}\to 0$ and $r^{(k)}\to \infty$.

12 pages. This is a substantially improved version. Accepted for publication in Physical Review E. Comments are welcome

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