Spring 2005: 18.325
The Mathematics and Applications of Finite Random Matrices
Professor Alan Edelman
T,R 11:00-12:30, Bldg. 2-143

Random Growth Processes

Simulation 1
Simulation 2

On the second Eigenvalue and Random Walks in Random d-Regular Graphs - Joel Friedman (pdf)
Random vicious walks and random matrices - Jinho Baik (pdf)
Random Growth and Random Matrices - Kurt Johansson (pdf)

Proofs of Semicircle Law

A simple approach to global regime of the random matrix theory -Pastrur (ps)
Some elementary results around the Wigner Semicircle law - Khorunzhy (pdf)

Random matrices with complex eigenvalues

Non-Hermitian random matrices - Khoruzhenko (pdf)
Eigenvalue curves of asymmetric tridiagonal random matrices - Khoruzhenko (pdf)
Regular spacings of complex eigenvalues in the one-dimensional non-Hermitian Anderson model - Khoruzhenko (pdf)

Functions for Random matrices

Correlation Functions, Cluster functions and Spacing distributions for Random Matrices - Tracy and Widom (pdf)

Random matrices and PCA

On the distribution of the largest principal component - Johnstone (pdf)

Random matrices and Financial Analysis

Exponential weighting and RMT based Filtering of Financial Covariance Matrices - Pafka, Potters, and Kondor (pdf)
Noise dressing of financial correlation matrices - Laloux, Cizeau, et al (pdf)
Random matrix theory and financial correlations - Laoux, Cizeau and Potters (pdf)
Rational decisions, random matrices and spin glasses - Gallucio, Bouchaud and Potters (pdf)
Universal and nonuniversal properties of cross correlations in financial time series = Plerou et al (pdf)
Random matrix approach to cross correlations in financial data - Plerou et al (pdf)

Random matrices and the Replica Method

Asymptotic corrects to the Wigner semicircular law using the replica method - Dhesi and Jones (pdf)
PCA using the replica method - Hoyle and Rattray (pdf)

Communication Theory

Multiuser receivers, random matrices, and free probability - David Tse (pdf)
Random Matrices and Wireless Communications - Tulino and Verdu (pdf)
Asymptotic eigenvalue moments for linear multiuser detection - Sergio Verdu (pdf)
Statistical analysis of the capacity of MIMO frequency selective rayleigh fading channels - Scaglione (pdf)
The statistics of the MIMO frequency selective fading AWGN Channel Capacity - Scaglione (pdf)
Capacity of multi-antenna gaussian channels - Telatar (pdf)
Complex random matrices and rayleigh channel capacity - Ratnarajah and Vaillancourt (pdf)
Spectral efficiencty of CDMA with random spreading - Verdu and Shamai (pdf)
Upper bounds on the Bit-Error Rate of Optimum Combining in Wireless Systems - Winters and Salz (pdf)
Bounds and Approximations for Optimum Combining of Signals - Chiani and Win (pdf)

Environmental Issues for MIMO Capacity - Bliss and Forsythe (pdf)

Free Probability and Addition of Random Matrices

Multiuser receivers, random matrices, and free probability - David Tse (pdf)
Free probability theory and random matrices - Roland Speicher (pdf)
On the law of addition of random matrices - Pastur and Vasilchuk (pdf)
Law of addition in random matrix theory - Zee (pdf)

Finite Fields

Random matrix theory over finite fields - Jason Fulman (pdf)

Array Signal Processing

Inferring the eigenvalues of covariance matrices from limited, noisy data - Everson and Roberts (pdf)

Random Networks

Eigenvalues of random power law graphs - Chung, Lu, and Vu (pdf)
The Web as a graph: measurements, models and methods - Kleinberg, et. al (pdf)
The spectra of random graphs with given expected degrees - Chung, Lu and Vu (pdf)
Spectra and eigenvectors of scale-free networks - Goh, Kahng, and Kim (pdf)
Spectra of real world graphs - Farkas, et. al. (pdf)

Random Graphs

Eigenvalues of random power law graphs - Chung, Lu, and Vu (pdf)
The spectra of random graphs with given expected degrees - Chung, Lu and Vu (pdf)
Spectra of real world graphs - Farkas, et. al (pdf)

Computational Biology

Theoretical limitations of massively parallel biology - Szallasi, Periwal, et. al. (ppt)
RNA folding and large N matrix theory - Zee (pdf)

Last modified 1/05/2004 by raj (AT) mit.edu