Limit Theorems for Maximal and Minimal Eigenvalues of Random Matrices

1991 ◽  
Vol 35 (4) ◽  
pp. 680-695 ◽  
Author(s):  
V. L. Girko
Keyword(s):  
Random Matrices ◽  
Limit Theorems ◽  
Eigenvalues Of Random Matrices

scholarly journals Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

2014 ◽  
Vol 329 (2) ◽  
pp. 641-686 ◽  
Author(s):  
Florent Benaych-Georges ◽  
Alice Guionnet ◽  
Camille Male
Keyword(s):  
Random Matrices ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Linear Statistics ◽  
Heavy Tailed

scholarly journals Small-Deviation Inequalities for Sums of Random Matrices

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 638
Author(s):  
Xianjie Gao ◽  
Chao Zhang ◽  
Hongwei Zhang
Keyword(s):  
Random Matrices ◽  
Large Deviation ◽  
Small Deviation ◽  
High Dimensional ◽  
Main Research ◽  
Infinite Dimensional ◽  
The Matrix ◽  
Largest Eigenvalues ◽  
Deviation Inequalities ◽  
Eigenvalues Of Random Matrices

Random matrices have played an important role in many fields including machine learning, quantum information theory, and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices. Although there are intensive studies on the large-deviation inequalities for random matrices, only a few works discuss the small-deviation behavior of random matrices. In this paper, we present the small-deviation inequalities for the largest eigenvalues of sums of random matrices. Since the resulting inequalities are independent of the matrix dimension, they are applicable to high-dimensional and even the infinite-dimensional cases.

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