RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE

By Ke Wang. 2011

49 citations recorded by the source corpus.

We study the universality of the eigenvalue statistics of the covariance matrices $\frac{1}{n}M^* M$ where M is a large p × n matrix with independent entries that have mean zero, variance one and sufficiently high finite moments. In particular, as an application, we prove a variant of universality results regarding the smallest singular value of Mp, n. This paper is an extension of the results of Tao and Vu (2009) from the bulk of the spectrum up to the edge.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/90d9f2b0407152c816d5574b86581c5b7c5e8348

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Natesh S. Pillai
2. Jun Yin
3. Z. Bao
4. Guangming Pan
5. Wang Zhou
6. Debashis Paul
7. Alexander Aue
8. Dan Romik

In Mathematical Physics

1. Natesh S. Pillai
2. Z. Bao
3. Jun Yin
4. Guangming Pan
5. Wang Zhou
6. Debashis Paul
7. Alexander Aue
8. Xiucai Ding

In Statistics and Probability

1. Z. Bao
2. Guangming Pan
3. Natesh S. Pillai
4. Wang Zhou
5. Jun Yin
6. Xiucai Ding
7. Alexander Aue
8. Debashis Paul

Citations in the corpus

• Universality of covariance matrices (2011, background): “[3] Zhigang Bao, Guangming Pan, and Wang Zhou.”
• Random matrix theory in statistics: A review (2014, background): “Tao and Vu (2010b) and Wang (2012) proved the universality of local eigenvalue statistics at the edge of the spectrum for the Wigner and Wishart cases, respectively.”
• Tracy-Widom law for the extreme eigenvalues of sample correlation matrices (2011, unknown): “We remark here that we consider the domain [L1, L2] = [a/2 − , 2b + ] rather than [a, b] in [20].”
• The Surprising Mathematics of Longest Increasing Subsequences (2015, background): “This was proved in various levels of generality in [97], [99], [122], [144].”
• Universality for the largest eigenvalue of sample covariance matrices with general population (2013, methodology): “The delocalization property for the eigenvectors of random matrices was also raised in [12] and improved in the series work [13, 14, 19] for Wigner matrices and extended to sample covariance matrices in [35, 39, 16, 31], which asserts that the coefficients of the unit eigenvectors are in the order o”