Restricted isometry property for random matrices with heavy-tailed columns

2014 ◽  
Vol 352 (5) ◽  
pp. 431-434 ◽  
Author(s):  
Olivier Guédon ◽  
Alexander E. Litvak ◽  
Alain Pajor ◽  
Nicole Tomczak-Jaegermann
Keyword(s):  
Random Matrices ◽  
Restricted Isometry Property ◽  
Heavy Tailed

The restricted isometry property for random matrices with ϕ-subgaussian entries

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Yuriy Kozachenko ◽  
Viktor Troshki
Keyword(s):  
Random Matrices ◽  
Restricted Isometry Property

AbstractThe aim of this article is to construct the generalized random matrices, which satisfies the restricted isometry property (as introduced by Candes and Tao). Let the data be presented as a product of a vector with not more than

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 Heavy-tailed random matrices

2018 ◽  
Author(s):  
Vladimir Kravtsov
Keyword(s):  
Random Matrices ◽  
Heavy Tails ◽  
Probability Distributions ◽  
Basin Of Attraction ◽  
Random Variables ◽  
Universal Properties ◽  
Random Matrix Ensembles ◽  
Free Random Variables ◽  
Heavy Tailed ◽  
Non Gaussian

This article considers non-Gaussian random matrices consisting of random variables with heavy-tailed probability distributions. In probability theory heavy tails of distributions describe rare but violent events which usually have a dominant influence on the statistics. Furthermore, they completely change the universal properties of eigenvalues and eigenvectors of random matrices. This article focuses on the universal macroscopic properties of Wigner matrices belonging to the Lévy basin of attraction, matrices representing stable free random variables, and a class of heavy-tailed matrices obtained by parametric deformations of standard ensembles. It first examines the properties of heavy-tailed symmetric matrices known as Wigner–Lévy matrices before discussing free random variables and free Lévy matrices as well as heavy-tailed deformations. In particular, it describes random matrix ensembles obtained from standard ensembles by a reweighting of the probability measure. It also analyses several matrix models belonging to heavy-tailed random matrices and presents methods for integrating them.

scholarly journals Localization and delocalization of eigenvectors for heavy-tailed random matrices

2013 ◽  
Vol 157 (3-4) ◽  
pp. 885-953 ◽  
Author(s):  
Charles Bordenave ◽  
Alice Guionnet
Keyword(s):  
Random Matrices ◽  
Heavy Tailed

scholarly journals Delocalization at Small Energy for Heavy-Tailed Random Matrices

2017 ◽  
Vol 354 (1) ◽  
pp. 115-159 ◽  
Author(s):  
Charles Bordenave ◽  
Alice Guionnet
Keyword(s):  
Random Matrices ◽  
Small Energy ◽  
Heavy Tailed

scholarly journals Spectrum of Non-Hermitian Heavy Tailed Random Matrices

2011 ◽  
Vol 307 (2) ◽  
pp. 513-560 ◽  
Author(s):  
Charles Bordenave ◽  
Pietro Caputo ◽  
Djalil Chafaï
Keyword(s):  
Random Matrices ◽  
Heavy Tailed

scholarly journals The Spectrum of Heavy Tailed Random Matrices

2007 ◽  
Vol 278 (3) ◽  
pp. 715-751 ◽  
Author(s):  
Gérard Ben Arous ◽  
Alice Guionnet
Keyword(s):  
Random Matrices ◽  
Heavy Tailed
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