Updated: June 8th, 2024 05:45

2023 article

Analysis of the Limiting Spectral Distribution of Large-dimensional General Information-Plus-Noise-Type Matrices

Zhou, H., Hu, J., Bai, Z., & Silverstein, J. W. (2023, July 28). *JOURNAL OF THEORETICAL PROBABILITY*, Vol. 7.

Sources: ORCID, Web Of Science, NC State University Libraries

Added: July 29, 2023

2022 journal article

A tribute to PR Krishnaiah

*JOURNAL OF MULTIVARIATE ANALYSIS*, *188*.

author keywords: GIC of model selection; Image reconstruction; Prof. Krishnaiah; Random matrices

TL;DR:
The authors reminisce on their association with P.R. Krishnaiah, mainly involving the behavior of eigenvalues of random matrices, and outline two areas of applied work he performed with one of the authors.
(via Semantic Scholar)

Sources: ORCID, Web Of Science, NC State University Libraries

Added: September 6, 2021

2022 article

Limiting eigenvalue behavior of a class of large dimensional random matrices formed from a Hadamard product

Silverstein, J. W. (2022, July 28). *RANDOM MATRICES-THEORY AND APPLICATIONS*, Vol. 7.

author keywords: Eigenvalues of random matrices; Hadamard product; deterministic equivalent

Sources: Web Of Science, NC State University Libraries

Added: September 19, 2022

2022 journal article

Weak convergence of a collection of random functions defined by the eigenvectors of large dimensional random matrices

*RANDOM MATRICES-THEORY AND APPLICATIONS*, *11*(04).

Sources: ORCID, Web Of Science, NC State University Libraries

Added: February 22, 2022

2020 article

Local Convergence of an AMP Variant to the LASSO Solution in Finite Dimensions

(2020, July 18).

Source: ORCID

Added: November 7, 2020

2020 article

Weak Convergence of a Collection of Random Functions Defined by the Eigenvectors of Large Dimensional Random Matrices

(2020, December 23).

Source: ORCID

Added: December 25, 2020

2019 journal article

Singular values of large non-central random matrices

*Random Matrices: Theory and Applications*, *6*, 2050012.

author keywords: Non-central random matrices; singular values; asymptotic normality

Sources: Crossref, NC State University Libraries

Added: July 6, 2020

2015 journal article

The random matrix regime of Maronna's M-estimator with elliptically distributed samples

*JOURNAL OF MULTIVARIATE ANALYSIS*, *139*, 56–78.

author keywords: Random matrix theory; Robust estimation; Elliptical distribution

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2014 journal article

A note on the CLT of the LSS for sample covariance matrix from a spiked population model

*JOURNAL OF MULTIVARIATE ANALYSIS*, *130*, 194–207.

author keywords: Large-dimensional sample covariance matrices; Spiked population model; Central limit theorem; Centering parameter; Factor models

TL;DR:
An asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance structure is established.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2014 journal article

Robust Estimates of Covariance Matrices in the Large Dimensional Regime

*IEEE TRANSACTIONS ON INFORMATION THEORY*, *60*(11), 7269–7278.

author keywords: Robust estimation; random matrix theory

TL;DR:
It is proved that, for sample vectors made of independent entries having some moment conditions, the difference between the sample covariance matrix and (a scaled version of) such robust estimator tends to zero in spectral norm, almost surely.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2013 conference paper

A joint robust estimation and random matrix framework with application to array processing

*2013 IEEE International Conference on Acoustics, Speech and Signal Processing*. Presented at the ICASSP 2013 - 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

Event: ICASSP 2013 - 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Sources: Crossref, NC State University Libraries

Added: August 24, 2020

2013 journal article

Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulations

*THEORETICAL POPULATION BIOLOGY*, *89*, 34–43.

author keywords: Principal components analysis; Eigenanalysis; Population structure; Eigenvalues; Number of subpopulations

MeSH headings : Genetics, Population; Genotype; Humans; Models, Theoretical

TL;DR:
A mathematical model is presented that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of subpopulations represented in the data.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2012 journal article

A CLT FOR INFORMATION-THEORETIC STATISTICS OF NON-CENTERED GRAM RANDOM MATRICES

*Random Matrices: Theory and Applications*, *01*(02), 1150010.

Sources: Crossref, NC State University Libraries

Added: August 24, 2020

2012 journal article

NO EIGENVALUES OUTSIDE THE SUPPORT OF THE LIMITING SPECTRAL DISTRIBUTION OF INFORMATION-PLUS-NOISE TYPE MATRICES

*Random Matrices: Theory and Applications*, *01*(01), 1150004.

author keywords: Empirical spectral distribution; Stieltjes transform; information-plus-noise model

Sources: Crossref, NC State University Libraries

Added: August 24, 2020

2011 journal article

A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels

*IEEE Transactions on Information Theory*, *57*(6), 3493–3514.

author keywords: Deterministic equivalent; ergodic capacity; MAC; MIMO; optimal precoder; random matrix theory

TL;DR:
Novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices are provided for the ergodic rate region of multiple antenna multiple access channels, when each point-to-point propagation channel is modelled according to the Kronecker model.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

6. Clean Water and Sanitation
(OpenAlex)

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries, Crossref

Added: August 6, 2018

2011 article

Eigen-Inference for Energy Estimation of Multiple Sources

Couillet, R., Silverstein, J. W., Bai, Z., & Debbah, M. (2011, April). *IEEE TRANSACTIONS ON INFORMATION THEORY*, Vol. 57, pp. 2420–2439.

author keywords: Cognitive radio; G-estimation; power estimation; random matrix theory; statistical inference

TL;DR:
In this paper, a new method is introduced to blindly estimate the transmit power of multiple signal sources in multiantenna fading channels, when the number of sensing devices and thenumber of available samples are sufficiently large compared to theNumber of sources.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

7. Affordable and Clean Energy
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2011 chapter

Random Matrix Theory

In *International Encyclopedia of Statistical Science* (pp. 1168–1170).

Sources: Crossref, NC State University Libraries

Added: August 24, 2020

2010 conference paper

Eigen-inference for multi-source power estimation

*2010 IEEE International Symposium on Information Theory*. Presented at the 2010 IEEE International Symposium on Information Theory - ISIT.

Event: 2010 IEEE International Symposium on Information Theory - ISIT

Sources: Crossref, NC State University Libraries

Added: August 24, 2020

2010 journal article

Fundamental Limit of Sample Generalized Eigenvalue Based Detection of Signals in Noise Using Relatively Few Signal-Bearing and Noise-Only Samples

*IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING*, *4*(3), 468–480.

author keywords: Multivariate F distribution; random matrices; sample covariance matrix; signal detection; Wishart distribution

TL;DR:
A fundamental asymptotic limit of sample generalized eigenvalue-based detection of signals in arbitrarily colored noise when there are relatively few signal bearing and noise-only samples is proved.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2010 book

Spectral Analysis of Large Dimensional Random Matrices

(2nd ed.). New York: Springer.

Sources: NC State University Libraries, ORCID

Added: October 29, 2020

2009 conference paper

Asymptotic capacity of multi-user MIMO communications

*2009 IEEE Information Theory Workshop*. Presented at the 2009 IEEE Information Theory Workshop (ITW 2009).

Event: 2009 IEEE Information Theory Workshop (ITW 2009)

Sources: Crossref, NC State University Libraries

Added: August 24, 2020

2009 journal article

No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix

*JOURNAL OF MULTIVARIATE ANALYSIS*, *100*(1), 37–57.

author keywords: Empirical spectral distribution; Stieltjes transform; Separable covariance; CDMA; MIMO

TL;DR:
It is shown that, under appropriate conditions on the eigenvalues of A"n and B"n, with probability 1, there will be no eigen values in any closed interval outside the support of the limiting distribution, for sufficiently large n.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2009 conference paper

Rate region of correlated MIMO multiple access channels and broadcast channels

*2009 IEEE/SP 15th Workshop on Statistical Signal Processing*. Presented at the 2009 IEEE/SP 15th Workshop on Statistical Signal Processing (SSP).

Event: 2009 IEEE/SP 15th Workshop on Statistical Signal Processing (SSP)

Sources: Crossref, NC State University Libraries

Added: August 24, 2020

2009 chapter

THE STIELTJES TRANSFORM AND ITS ROLE IN EIGENVALUE BEHAVIOR OF LARGE DIMENSIONAL RANDOM MATRICES

In *Random Matrix Theory and Its Applications* (pp. 1–25).

Sources: Crossref, NC State University Libraries

Added: August 24, 2020

2007 journal article

Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices

*JOURNAL OF MULTIVARIATE ANALYSIS*, *98*(6), 1099–1122.

author keywords: random matrix; empirical distribution function of eigenvalues; Stieltjes transform

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2007 conference paper

Fundamental Limit of Sample Eigenvalue based Detection of Signals in Colored Noise using Relatively Few Samples

*2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers*. Presented at the 2007 41st Asilomar conference on Signals, Systems and Computers (ACSSC).

Event: 2007 41st Asilomar conference on Signals, Systems and Computers (ACSSC)

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

2007 journal article

On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices

*JOURNAL OF MULTIVARIATE ANALYSIS*, *98*(4), 678–694.

author keywords: random matrix; empirical distribution function of eigenvalues; Stieltjes transform

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2007 journal article

On the signal-to-interference ratio of CDMA systems in wireless communications

*ANNALS OF APPLIED PROBABILITY*, *17*(1), 81–101.

author keywords: code-division multiple access (CDMA) systems; random matrix; empirical distributions

TL;DR:
It is proven that, with probability 1, $SIR_1$ tends, as $N\to\infty$, to the limit of the nonrandom, Hermitian positive definite matrix A, which represents the best signal-to-interference ratio for user 1 with respect to the other $K-1$ users in a direct-sequence code-division multiple-access system in wireless communications.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2006 journal article

Eigenvalues of large sample covariance matrices of spiked population models

*JOURNAL OF MULTIVARIATE ANALYSIS*, *97*(6), 1382–1408.

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2006 journal article

Gaussian fluctuations for non-Hermitian random matrix ensembles

*ANNALS OF PROBABILITY*, *34*(6), 2118–2143.

author keywords: random matrix theory; central limit theorem; spectral statistics

UN Sustainable Development Goal Categories

16. Peace, Justice and Strong Institutions
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: August 6, 2018

2006 book

Spectral Analysis of Large Dimensional Random Matrices

(1st ed.). New York / Beijing: Springer / Science Press.

Sources: NC State University Libraries, ORCID

Added: October 29, 2020

2006 conference paper

Theory of Large Dimensional Random Matrices for Engineers

*2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications*. Presented at the 2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications.

Event: 2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

2004 journal article

CLT for linear spectral statistics of large-dimensional sample covariance matrices

*Annals of Probability*, *32*(1A), 553–605.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1999 journal article

Exact separation of eigenvalues of large dimensional sample covariance matrices

*Annals of Probability*, *27*(3), 1536–1555.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1999 journal article

Methodologies in spectral analysis of large dimensional random matrices, a review - Comment: Complements and new developments

*Statistica Sinica*, *9*(3), 667–671.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1998 journal article

No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices

*Annals of Probability*, *26*(1), 316–345.

Sources: NC State University Libraries, NC State University Libraries

Added: August 6, 2018

1995 journal article

Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices

*Journal of Multivariate Analysis*, *54*(2), 295–309.

author keywords: EIGENVALUES OF RANDOM MATRICES; SPECTRAL DISTRIBUTION; STIELTJES TRANSFORM

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

1995 journal article

On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices

*Journal of Multivariate Analysis*, *54*(2), 175–192.

author keywords: RANDOM MATRIX; EMPIRICAL DISTRIBUTION FUNCTION OF EIGENVALUES; STIELTJES TRANSFORM

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

1995 journal article

Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices

*Journal of Multivariate Analysis*, *55*(2), 331–339.

author keywords: random matrix; empirical distribution function of eigenvalues; Stieltjes transform

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

1994 journal article

The spectral radii and norms of large dimensional non-central random matrices

*Communications in Statistics. Stochastic Models*, *10*(3), 525–532.

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

1992 conference paper

Large dimensional random matrix theory for signal detection and estimation in array processing

*[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing*, 276–279.

Event: [1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing at Victoria, British Columbia, Canada on October 7-9, 1992

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

1992 journal article

Signal detection via spectral theory of large dimensional random matrices

*IEEE Transactions on Signal Processing*, *40*(8), 2100–2105.

Sources: Crossref, NC State University Libraries

Added: August 29, 2019

1990 report

Spectral theory of large dimensional random matrices applied to signal detection

[Technical Report.].

Sources: NC State University Libraries, ORCID

Added: November 5, 2020

1990 journal article

Weak Convergence of Random Functions Defined by The Eigenvectors of Sample Covariance Matrices

*The Annals of Probability*, *18*(3), 1174–1194.

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

1989 journal article

On the eigenvectors of large dimensional sample covariance matrices

*Journal of Multivariate Analysis*, *30*(1), 1–16.

Sources: Crossref, NC State University Libraries

Added: August 25, 2020

1989 journal article

On the weak limit of the largest eigenvalue of a large dimensional sample covariance matrix

*Journal of Multivariate Analysis*, *30*(2), 307–311.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1988 journal article

A note on the largest eigenvalue of a large dimensional sample covariance matrix

*Journal of Multivariate Analysis*, *26*(2), 166–168.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1986 journal article

Eigenvalues and eigenvectors of large-dimensional sample covariance matrices

*Random Matrices and Their Applications*, *50*, 153–159.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1985 journal article

The Limiting Eigenvalue Distribution of a Multivariate F Matrix

*SIAM Journal on Mathematical Analysis*, *16*(3), 641–646.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1985 journal article

The Smallest Eigenvalue of a Large Dimensional Wishart Matrix

*The Annals of Probability*, *13*(4), 1364–1368.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1984 journal article

Comments on a result of Yin, Bai, and Krishnaiah for large dimensional multivariate F matrices

*Journal of Multivariate Analysis*, *15*(3), 408–409.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1984 report

On Limit of the Largest Eigenvalue of the Large Dimensional Sample Covariance Matrix.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1984 journal article

Some limit theorems on the eigenvectors of large dimensional sample covariance matrices

*Journal of Multivariate Analysis*, *15*(3), 295–324.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1981 journal article

A nonlinear system with singular vector field near equilibria

*Applicable Analysis*, *12*(1), 57–71.

Sources: Crossref, NC State University Libraries

Added: August 31, 2020

1981 journal article

Describing the Behavior of Eigenvectors of Random Matrices Using Sequences of Measures on Orthogonal Groups

*SIAM Journal on Mathematical Analysis*, *12*(2), 274–281.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1979 journal article

On the Randomness of Eigenvectors Generated from Networks with Random Topologies

*SIAM Journal on Applied Mathematics*, *37*(2), 235–245.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1978 report

On word classification using a neural network

(Pattern Analysis Report No. 43; Vol. 2; By U. Grenander). Providence, Rhode Island: Division of Applied Mathematics, Brown University.

Sources: NC State University Libraries, ORCID

Added: October 29, 2020

1978 report

Public key cryptosystems: an elementary overview

In *Confidentiality in Surveys* (Report No. 29). Stockholm, Sweden: Department of Statistics, University of Stockholm.

Sources: NC State University Libraries, ORCID

Added: August 25, 2020

1978 journal article

Reply to Grossberg.

*Psychological Review*, *85*(6), 597–603.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1977 journal article

Distinctive features, categorical perception, and probability learning: Some applications of a neural model.

*Psychological Review*, *84*(5), 413–451.

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1977 journal article

Spectral Analysis of Networks with Random Topologies

*SIAM Journal on Applied Mathematics*, *32*(2), 499–519.

UN Sustainable Development Goal Categories

16. Peace, Justice and Strong Institutions
(OpenAlex)

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1977 report

Stability analysis and correction of pathological behavior of neural networks

(Pattern Analysis Report No. 48). Providence, Rhode Island: Division of Applied Mathematics, Brown University.

Sources: NC State University Libraries, ORCID

Added: October 29, 2020

1977 conference paper

Vowel pre-processing with a neurally based model

*ICASSP '77. IEEE International Conference on Acoustics, Speech, and Signal Processing*. Presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing.

Event: IEEE International Conference on Acoustics, Speech, and Signal Processing

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1976 journal article

Asymptotics applied to a neural network

*Biological Cybernetics*, *22*(2), 73–84.

MeSH headings : Cognition; Mathematics; Models, Neurological; Nervous System Physiological Phenomena; Neural Pathways / physiology

TL;DR:
A mathematical model of neural processing is proposed which incorporates a theory for the storage of information that lends support to a distributive theory of memory using synaptic modification.
(via Semantic Scholar)

Sources: Crossref, NC State University Libraries

Added: October 29, 2020

1976 journal article

Preprocessing with a simple neural model

*Neuroscience Abstracts*, *2*(618), 438.

Sources: NC State University Libraries, ORCID

Added: October 29, 2020

report

Comments on ‘A Unitary Transformation Method for Angle-of-Arrival Estimation’

Combettes, P. L., & Silverstein, J. [Technical Report].

Source: NC State University Libraries

Added: August 25, 2020

report

Comments on ‘A Unitary Transformation Method for Angle-of-Arrival Estimation’

Combettes, P. L., & Silverstein, J. *Comments on ‘A Unitary Transformation Method for Angle-of-Arrival Estimation.’*

Source: ORCID

Added: November 6, 2020

report

On the rectification of covariance matrices

Combettes, P. L., & Silverstein, J. [Technical Report].

Source: NC State University Libraries

Added: August 25, 2020

report

On the rectification of covariance matrices

Combettes, P. L., & Silverstein, J.

Source: ORCID

Added: November 6, 2020

Updated: July 17th, 2020 18:46

1978 - present

1975 - 1978

Updated: July 17th, 2020 18:47

1971 - 1975

1967 - 1971

Funding history based on the linked ORCID record. Updated: November 6th, 2020 07:43

grant
June 1, 2009 - May 1, 2012

Spiked Models of Large Dimensional Random Matrices Applied to Wireless Communications and Array Signal Processing

Army Research Office

grant
June 1, 2005 - May 1, 2009

Eigenvalues of Large Dimensional Random Matrices in Wireless Communications and Array Signal Processing

Army Research Office

grant
July 15, 1997 - June 30, 2001

Spectral Behavior of Two Classes of Large Dimensional Random Matrices

Directorate for Mathematical & Physical Sciences

grant
July 1, 1994 - June 30, 1997

Spectral Theory of Large Dimensional Random Matrices and Its Applications

Directorate for Mathematical & Physical Sciences

grant
June 15, 1989 - May 31, 1993

Mathematical Sciences: The Spectral Behavior of Large Dimensional Random Matrices Applied to Signal Processing

Directorate for Mathematical & Physical Sciences

grant
June 1, 1986 - May 31, 1989

Mathematical Sciences: The Behavior of Eigenvectors of LargeDimensional Sample Covariance Matrices

Directorate for Mathematical & Physical Sciences

grant
June 1, 1983 - May 1, 1985

An Invariance Principle on the Eigenvectors of Large Dimensional Sample Covariance Matrices

Directorate for Mathematical and Physical Sciences

grant
June 1, 1981 - May 30, 1982

Describing the Behavior of Eigenvectors of Large Dimensional Random Matrices

Directorate for Mathematical & Physical Sciences

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