Random matrices: The distribution of the smallest singular values

Terence Tao, Van Vu

Type: Preprint

Publication Date: 2009-01-01

Citations: 6

DOI: https://doi.org/10.48550/arxiv.0903.0614

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
+	Random Matrices: The circular Law	2007	Terence Tao Van Vu
+ PDF Chat	RANDOM MATRICES: THE CIRCULAR LAW	2008	Terence Tao Van Vu
+ PDF Chat	Random Matrices: the Distribution of the Smallest Singular Values	2010	Terence Tao Van Vu
+	On the smallest singular value of symmetric random matrices	2020	Vishesh Jain Ashwin Sah Mehtaab Sawhney
+	On the smallest singular value of symmetric random matrices	2020	Vishesh Jain Ashwin Sah Mehtaab Sawhney
+	The smallest singular value of random combinatorial matrices	2020	Tuan Tran
+ PDF Chat	On the smallest singular value of symmetric random matrices	2021	Vishesh Jain Ashwin Sah Mehtaab Sawhney
+	The limit of the smallest singular value of random matrices with i.i.d. entries	2014	Konstantin Tikhomirov
+	The limit of the smallest singular value of random matrices with i.i.d. entries	2014	Konstantin Tikhomirov
+	The smallest singular value of random rectangular matrices with no moment assumptions on entries	2014	Konstantin Tikhomirov
+	The smallest singular value of random rectangular matrices with no moment assumptions on entries	2014	Konstantin Tikhomirov
+ PDF Chat	The smallest singular value for rectangular random matrices with L\'evy entries	2024	Y. F. Han
+	The least singular value of a random symmetric matrix	2022	Marcelo Campos Matthew Jenssen Marcus Michelen Julian Sahasrabudhe
+ 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 Chat	Asymptotic Behavior of the Maximum and Minimum Singular Value of Random Vandermonde Matrices	2012	Gabriel H. Tucci Philip Whiting
+	The Littlewood-Offord Problem and invertibility of random matrices	2007	Mark Rudelson Roman Vershynin
+	The Littlewood-Offord Problem and invertibility of random matrices	2007	Mark Rudelson Roman Vershynin
+ PDF Chat	The smallest singular value of random rectangular matrices with no moment assumptions on entries	2016	Konstantin Tikhomirov
+	Approximate Spielman-Teng theorems for the least singular value of random combinatorial matrices	2019	Vishesh Jain
+	Quantitative invertibility of random matrices: a combinatorial perspective	2019	Vishesh Jain

Works That Cite This (6)

Action	Title	Year	Authors
+	Eigenvectors of random graphs: Nodal domains	2008	Yael Dekel James R. Lee Nathan Linial
+	A universality result for the smallest eigenvalues of certain sample covariance matrices	2008	Ohad N. Feldheim Sasha Sodin
+	Cross-Validation for Unsupervised Learning	2009	Patrick O. Perry
+	Characteristic Polynomials of Sample Covariance Matrices	2009	Holger Kösters
+ PDF Chat	Characteristic Polynomials of Sample Covariance Matrices	2010	Holger Kösters
+ PDF Chat	Data-Driven Pattern Identification and Outlier Detection in Time Series	2018	Abdolrahman Khoshrou Eric Pauwels

Works Cited by This (29)

Action	Title	Year	Authors
+ PDF	The Concentration of Measure Phenomenon	2005	Michel Ledoux
+ 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
+	None	2002	Alexander Soshnikov
+	The distribution and moments of the smallest eigenvalue of a random matrix of wishart type	1991	Alan Edelman
+ PDF	Eigenvalues and Condition Numbers of Random Matrices	1988	Alan Edelman
+ PDF	Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung	1922	J. W. Lindeberg
+	Laguerre ensembles of random matrices: Nonuniversal correlation functions	1993	Taro Nagao Keith Slevin
+	Smallest singular value of random matrices and geometry of random polytopes	2004	A.E. Litvak Alain Pajor Mark Rudelson Nicole Tomczak-Jaegermann
+ PDF Chat	The condition number of a randomly perturbed matrix	2007	Van H. Vu Terence Tao