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Extreme eigenvalue statistics of m-dependent heavy- tailed matrices

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 α∈(0, 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.

Dependent random matrices , Heavy-tailed random matrices , Largest eigenvalue , marked Poisson process , Poisson cluster process , regular variation , Sample covariance matrix , Wigner matrix

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