Random matrices: Universality of ESDs and the circular law

Terence Tao, Van Vu, Manjunath Krishnapur

Type: Preprint

Publication Date: 2008-01-01

Citations: 18

DOI: https://doi.org/10.48550/arxiv.0807.4898

View Publication

Locations

arXiv (Cornell University) - View
DataCite API - View
arXiv (Cornell University) - View
DataCite API - View
arXiv (Cornell University) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF	Random matrices: Universality of ESDs and the circular law	2010	Terence Tao Van Vu Manjunath Krishnapur
+ PDF	From the Littlewood-Offord problem to the Circular Law: Universality of the spectral distribution of random matrices	2009	Terence Tao Van Vu
+	The circular law for sparse non-Hermitian matrices	2017	Anirban Basak Mark Rudelson
+	Random Matrices: The circular Law	2007	Terence Tao Van Vu
+	The circular law for sparse non-Hermitian matrices	2017	Anirban Basak Mark Rudelson
+ PDF	The circular law for sparse non-Hermitian matrices	2019	Anirban Basak Mark Rudelson
+	From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices	2008	Terence Tao Van Vu
+ PDF Chat	RANDOM MATRICES: THE CIRCULAR LAW	2008	Terence Tao Van Vu
+ PDF	Universality and the circular law for sparse random matrices	2012	Philip Matchett Wood
+	Circular law for random discrete matrices of given row sum	2012	Hoi H. Nguyen Van Vu
+	Circular law for random discrete matrices of given row sum	2012	Hoi H. Nguyen Van Vu
+	Universality of the ESD for a fixed matrix plus small random noise: a stability approach	2014	Philip Matchett Wood
+	Universality of the ESD for a fixed matrix plus small random noise: a stability approach	2014	Philip Matchett Wood
+	Local circular law for the product of a deterministic matrix with a random matrix	2017	Haokai Xi Fan Yang Jun Yin
+ PDF	Local circular law for random matrices	2013	Paul Bourgade Horng‐Tzer Yau Jun Yin
+	Local law for the product of independent non-Hermitian matrices with independent entries	2015	Yuriy Nemish
+	Local law for the product of independent non-Hermitian matrices with independent entries	2015	Yuriy Nemish
+	The Elliptic Law	2012	Hoi H. Nguyen Sean O’Rourke
+	The Elliptic Law	2012	Hoi H. Nguyen Sean O’Rourke
+	Rate of convergence for non-Hermitian random matrices and their products	2020	Jonas Jalowy

Works That Cite This (17)

Action	Title	Year	Authors
+	On the spectral radius of a random matrix	2016	Charles Bordenave Pietro Caputo Djalil Chafaï Konstantin Tikhomirov
+	Random matrices: The distribution of the smallest singular values	2009	Terence Tao Van Vu
+	Limit Theorems for Beta-Jacobi Ensembles	2009	Tiefeng Jiang
+	Concentration of random determinants and permanent estimators	2009	Kevin Costello Van Vu
+ PDF Chat	Circular law, extreme singular values and potential theory	2009	Guangming Pan Zhou Wang
+ PDF	Circular law theorem for random Markov matrices	2011	Charles Bordenave Pietro Caputo Djalil Chafaï
+ PDF	Circular Law for Noncentral Random Matrices	2010	Djalil Chafaï
+ PDF	The Dirichlet Markov Ensemble	2009	Djalil Chafaï
+ PDF	Spectral radius of random matrices with independent entries	2021	Johannes Alt László Erdős Torben Krüger
+	Location of the spectrum of Kronecker random matrices	2017	Johannes Alt László Erdős Torben Krüger Yuriy Nemish

Works Cited by This (16)

Action	Title	Year	Authors
+ PDF	The least singular value of a random square matrix is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="normal">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>	2008	Mark Rudelson Roman Vershynin
+ PDF	Spectral Analysis of Large Dimensional Random Matrices	2009	Zhidong Bai Jack W. Silverstein
+	On the Circular Law	2007	А. Н. Тихомиров
+	On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices	2006	R. Brent Dozier Jack W. Silverstein
+ PDF	Eigenvalues and Condition Numbers of Random Matrices	1988	Alan Edelman
+	Statistical Ensembles of Complex, Quaternion, and Real Matrices	1965	J. Ginibre
+ PDF	Circular Law for Noncentral Random Matrices	2010	Djalil Chafaï
+ PDF	Inverse Littlewood–Offord theorems and the condition number of random discrete matrices	2009	Terence Tao Van H. Vu
+	On the spectrum of random matrices	1972	L. А. Pastur
+ PDF Chat	The condition number of a randomly perturbed matrix	2007	Van H. Vu Terence Tao