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Random Matrix Theory for Heavy-Tailed Time Series
- Source :
- Heiny, J 2019, ' Random Matrix Theory for Heavy-Tailed Time Series ', Journal of Mathematical Sciences, vol. 237, no. 5, pp. 652-666 . https://doi.org/10.1007/s10958-019-04191-3
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
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.
- Subjects :
- Statistics and Probability
Series (mathematics)
Applied Mathematics
General Mathematics
010102 general mathematics
Sample (statistics)
Covariance
01 natural sciences
010305 fluids & plasmas
Fourth moment
0103 physical sciences
Development (differential geometry)
Statistical physics
0101 mathematics
Focus (optics)
Random matrix
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 237
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi.dedup.....473b8e2fe4c6dbeedc9146eeb6e1b471