Extreme eigenvalue statistics of $m$-dependent heavy-tailed matrices

Bojan Basrak; Yeonok Cho; Johannes Heiny; Paul Jung

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arXiv · 1910.08511

Extreme eigenvalue statistics of $m$-dependent heavy-tailed matrices

Bojan Basrak·Yeonok Cho·Johannes Heiny·Paul Jung

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Abstract

We analyze the largest eigenvalue statistics of m-dependent heavy-tailed Wigner matrices as well as the associated sample covariance matrices having entry-wise regularly varying tail distributions with parameter $0<\alpha<4$. Our analysis extends results in the previous literature for the corresponding random matrices with independent entries above the diagonal, by allowing for m-dependence between the entries of a given matrix. We prove that the limiting point process of extreme eigenvalues is a Poisson cluster process.

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Bojan Basrak, Yeonok Cho, Johannes Heiny, Paul Jung. 2019-10-18. Extreme eigenvalue statistics of $m$-dependent heavy-tailed matrices. https://arxiv.org/abs/1910.08511

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