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Random Matrix Theory for Heavy-Tailed Time Series

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  • J. Heiny
This paper is a review of recent results for large random matrices with heavy-tailed entries. First, we outline the development of and some classical results in random matrix theory. We focus on large sample covariance matrices, their limiting spectral distributions, the asymptotic behavior of their largest and smallest eigenvalues and their eigenvectors. The limits significantly depend on the finite or infiniteness of the fourth moment of the entries of the random matrix. We compare the results for these two regimes which give rise to completely different asymptotic theories. Finally, the limits of the extreme eigenvalues of sample correlation matrices are examined.
Original languageEnglish
JournalJournal of Mathematical Sciences
Volume237
Issue5
Pages (from-to)652-666
Number of pages15
ISSN1072-3374
DOIs
Publication statusPublished - 2019

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