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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.… Click to show full 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)}→∞.
Keywords:
order spacing;
higher order;
universal scaling;
random matrices;
spacing ratios;
order
Journal Title: Physical review. E
Year Published: 2022
Link to full text (if available)
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Journal Title: Physical review. E
Year Published: 2022
Link to full text (if available)
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recommendations!