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

Higher-order spacing ratios are investigated analytically using a Wigner-like surmise for Gaussian ensembles of random matrices. For a kth 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) 0 and r(k) infinity.

Automated summary

This article analytically investigates higher-order spacing ratios using a Wigner-like surmise for Gaussian ensembles of random matrices. For a kth order spacing ratio (r(k), k > 1), the matrix of dimension 2k + 1 is considered. A universal scaling relation for this ratio, previously known from numerical studies, is proven in the asymptotic limits of r(k) approaching 0 and infinity.