Marchenko-Pastur law for tensor powers of exchangeable unconditional vectors

2026/07/23 by Feng Cheng, Dan Mikulincer
#math.PR #math.ST #stat.TH

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Abstract

Given an isotropic, exchangeable, and unconditional random vector \mathbf X, we consider the sample covariance matrix constructed from i.i.d. copies of several tensor models of \mathbf X, such as the tensor power X^{⊗ d}. Under appropriate moment conditions on \mathbf X, we show that almost surely, the empirical spectral distribution converges weakly to the Marchenko-Pastur law. This extends previous results which required the coordinates of \mathbf X to be independent. As we demonstrate, our extension applies to many new random vectors \mathbf X of interest.

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