Author

Xuechun Hu

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Preprint Aug 2026

Characteristic polynomial of self-normalized random matrices

We study the characteristic polynomial of self-normalized random matrices, whose rows are independent and normalized to have unit $\mathrm{L}^2$ norm. The entries before normalization are assumed to have regularly varying tails with tail index $\alpha \in [0,2]$. We prove that, outside the unit disk, the characteristic...

Quentin François, J. Heiny, Xuechun Hu · 0 citations

Preprint Aug 2026

Non-Gaussian fluctuations for traces of squared sample correlation matrices in high dimensions

We provide limit theory for the trace of the squared sample correlation matrix $\mathbf R$, constructed from $n$ observations of a $p$-dimensional random vector with iid components. If the entries have finite fourth moment and $p$ and $n$ grow proportionally, it is known that $\operatorname{tr}({\mathbf R}^2)$ satisfie...

J. Heiny, Xuechun Hu, Felix J. Seo · 0 citations