Random Matrix Theory for Heavy-Tailed Time Series
- Authors: Heiny J.1
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Affiliations:
- Department of Mathematics, Aarhus University
- Issue: Vol 237, No 5 (2019)
- Pages: 652-666
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242422
- DOI: https://doi.org/10.1007/s10958-019-04191-3
- ID: 242422
Cite item
Abstract
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, and 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.
About the authors
J. Heiny
Department of Mathematics, Aarhus University
Author for correspondence.
Email: johannes.heiny@math.au.dk
Denmark, Aarhus