Random Matrices and U-Statistics
Probability
2026-03-20 v2
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.
Cite
@article{arxiv.2509.25551,
title = {Random Matrices and U-Statistics},
author = {Florent Benaych-Georges and Tomas Espana},
journal= {arXiv preprint arXiv:2509.25551},
year = {2026}
}
Comments
15 pages, 1 figure