scholarly journals Truncated Linear Statistics Associated with the Top Eigenvalues of Random Matrices

2017 ◽  
Vol 167 (2) ◽  
pp. 234-259 ◽  
Author(s):  
Aurélien Grabsch ◽  
Satya N. Majumdar ◽  
Christophe Texier
Keyword(s):  
Random Matrices ◽  
Linear Statistics ◽  
Eigenvalues Of Random Matrices

scholarly journals Spectrum of SYK model II: Central limit theorem

2020 ◽  
pp. 2150037
Author(s):  
Renjie Feng ◽  
Gang. Tian ◽  
Dongyi. Wei
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Matrices ◽  
Central Limit ◽  
Almost Sure Convergence ◽  
Linear Statistics ◽  
The Central Limit Theorem ◽  
Eigenvalues Of Random Matrices ◽  
Global Density ◽  
Linear Statistics Of Eigenvalues

In our previous paper [R. Feng, G. Tian and D. Wei, Spectrum of SYK model, Peking Math. J. 2 (2019) 41–70], we derived the almost sure convergence of the global density of eigenvalues of random matrices of the SYK model. In this paper, we will prove the central limit theorem for the linear statistics of eigenvalues of the SYK model and compute its variance.

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

Pair dependent linear statistics for CβE

2020 ◽  
pp. 2150035
Author(s):  
Ander Aguirre ◽  
Alexander Soshnikov ◽  
Joshua Sumpter
Keyword(s):  
Zeta Function ◽  
Random Matrices ◽  
Riemann Zeta Function ◽  
Classical Result ◽  
Pair Correlation ◽  
Test Function ◽  
Linear Statistics ◽  
Smooth Test ◽  
Riemann Zeta ◽  
Counting Statistics

We study the limiting distribution of a pair counting statistics of the form [Formula: see text] for the circular [Formula: see text]-ensemble (C[Formula: see text]E) of random matrices for sufficiently smooth test function [Formula: see text] and [Formula: see text] For [Formula: see text] and [Formula: see text] our results are inspired by a classical result of Montgomery on pair correlation of zeros of Riemann zeta function.

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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