Random Matrix Theory and Its Applications

Readings

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

SES #	SURVEY PAPERS
1	Random 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
2	Proofs 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
3	Random 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
4	Functions for Random Matrices Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices - Tracy and Widom Shape Fluctuations and Random Matrices - Johansson
5	Random Matrices and PCA On the Distribution of the Largest Principal Component (PDF) - Johnstone
6	Communication 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
7	Free 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
8	Finite Fields Random Matrix Theory over Finite Fields (PDF) - Fulman
9	Array 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
10	Random 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.
11	Random 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.
12	Computational Biology Theoretical Limitations of Massively Parallel Biology - Szallasi, Periwal, et. al. RNA Folding and Large N Matrix Theory - Zee