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arXiv · 2509.25551

Random Matrices and U-Statistics

Florent Benaych-Georges·Tomas Espana
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Abstract

We introduce a family of coefficients based on U-statistics that generalize the notion of correlation and explore their properties in the large dimensional multivariate case, showing that in the null case of uncorrelated variables, the spectrum of generalized correlation matrices is distributed according to an affine transformation of the Mar\v{c}enko-Pastur law.

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Florent Benaych-Georges, Tomas Espana. 2025-09-29. Random Matrices and U-Statistics. https://arxiv.org/abs/2509.25551

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