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

Bhosale, Udaysinh T · Phys Rev E · 2023

basic_science · Level V

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Abstract

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)}→∞.