Courses:

Random Matrix Theory and Its Applications >> Content Detail



Study Materials



Readings

The readings and applets below were presented to the students during class.


SES #SURVEY PAPERS
1Random Growth Processes

Simulation 1

Simulation 2

On the Second Eigenvalue and Random Walks in Random d-Regular Graphs - Friedman

Random Vicious Walks and Random Matrices - Baik

Toeplitz Determinants, Random Growth and Determinantal Processes - Johansson
2Proofs of Semicircle Law

A Simple Approach to Global Regime of the Random Matrix Theory - Pastrur

Some Elementary Results around the Wigner Semicircle Law (PDF) - Khorunzhy
3Random Matrices with Complex Eigenvalues

Non-Hermition Random Matrices (PDF) - Khoruzhenko

Eigenvalue Curves of Asymmetric Tridiagonal Random Matrices - Khoruzhenko

Regular Spacings of Complex Eigenvalues in the One-Dimensional Non-Hermitian Anderson Model - Khoruzhenko
4Functions for Random Matrices

Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices - Tracy and Widom

Shape Fluctuations and Random Matrices - Johansson
5Random Matrices and PCA

On the Distribution of the Largest Principal Component (PDF) - Johnstone
6Communication Theory

Multiuser Receivers, Random Matrices, and Free Probability (PDF) - Tse

Asymptotic Eigenvalue Moments for Linear Multiuser Detection - Verdu

Statistical Analysis of the Capacity of MIMO Frequency Selective Reyleigh Fading Channels (PDF) - Scaglione

The Statistics of the MIMO Frequency Selective Fading AWGN Channel Capacity (PDF) - Scaglione

Capacity of Multi-antenna Gaussian Channels - Telatar

Complex Random Matrices and Reyleigh Channel Capacity (PDF) - Ratnarajah and Vaillancourt

Spectral Efficiency of CDMA with Random Spreading - Verdu and Shamai

Upper Bounds on the Bit-Error Rate of Optimum Combining in Wireless Systems - Winters and Salz

Bounds and Approximations for Optimum Combining of Signals in the Presence of Multiple Cochannel Interferers and Thermal Noise - Chiani and Win

Enviromental Issues for MIMO Capacity (PDF) - Bliss and Forsythe
7Free Probability and Addition of Random Matrices

Multiuser Receivers, Random Matrices, and Free Probability (PDF) - Tse

Free Probability Theory and Random Matrices (PS) - Speicher

On the Law of Addition of Random Matrices - Pastur and Vasilchuk

Law of Addition in Random Matrix Theory - Zee
8Finite Fields

Random Matrix Theory over Finite Fields (PDF) - Fulman
9Array Signal Processing

Inferring the Eigenvalues of Covariance Matrices from Limited, Noisy Data - Everson and Roberts

Large Dimensional Random Matrix Theory for Signal Detection and Estimation in Array Processing (PDF) - Silverstein and Combettes
10Random Networks

Eigenvalues of Random Power Law Graphs (PDF) - Chung, Lu, and Vu

The Web as a Graph: Measurements, Models and Methods - Kleinberg, et. al.

The Spectra of Random Graphs with Given Expected Degrees (PDF) - Chung, Lu, and Vu

Spectra and Eigenvectors of Scale-free Networks (PDF) - Goh, Kahng, and Kim

Spectra of Real World Graphs (PDF) - Farkas, et. al. 
11Random Graphs

Eigenvalues of Random Power Law Graphs (PDF) - Chung, Lu, and Vu

The Spectra of Random Graphs with Given Expected Degrees (PDF) - Chung, Lu, and Vu

Spectra of Real World Graphs (PDF) - Farkas, et. al.
12Computational Biology

Theoretical Limitations of Massively Parallel Biology - Szallasi, Periwal, et. al.

RNA Folding and Large N Matrix Theory - Zee

 








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