18.338J | Fall 2004 | Graduate
Infinite Random Matrix Theory

## Projects

### Mid-term Project

You will be asked to read a paper on a topic of interest to you that involves random matrix theory and present it via some mixture of the following perspectives:

• Write a description of greater clarity than the original publication, or

• Devise an improved solution to the problem under consideration, and write up your improvement (with appropriate discussion of the original solution).

• Implement the result in MATLAB® in order to study its performance in practice when the random matrices are finite. Considerations include choice of random matrix result, design of good tests, interpretation of results, and design and analysis of heuristics for improving performance in practice.

### Semester Project

The semester project can be an extension of the mid-term project if it sustains your interest. Otherwise, you will be asked to come up with some insights into a random matrix problem that is of interest to you.

Ideally, the topic you choose will be motivated by a computational problem you need to solve in your research. If the project is large, it may be tackled by a group. Otherwise, feel free to ask us for suggestions and ideas. Our goal is that you are able to get your hands wet trying to solve a problem while using computational and analytical tools that you’ve learned about.

In the past, a student’s whole PhD thesis came out of such an exploration. While that might be the exception and rather than the norm we hope we can instil a sense of adventure in you to tackle an interesting random matrix problem and to, hopefully, help you get some useful results out of it.

### Ideas for Projects

TOPICS RELATED PAPERS
Random Growth Processes On the Second Eigenvalue and Random Walks in Random d-Regular Graphs - Friedman

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

Random Matrices with Complex Eigenvalues Non-Hermition Random Matrices (PDF) - Khoruzhenko

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

Shape Fluctuations and Random Matrices - Johansson

Random Matrices and PCA On the Distribution of the Largest Principal Component (PDF) - Johnstone
Communication Theory Multiuser Receivers, Random Matrices, and Free Probability (PDF) - Tse

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 - Scaglione

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

Spectral Efficiency of CDMA with Random Spreading - Verdu and Shamai

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

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

Finite Fields Random Matrix Theory over Finite Fields (PDF) - Fulman
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

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.

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.

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

Financial Analysis Exponential Weighting and Random-Matrix-Theory-Based Filtering of Financial Covariance Matrices for Portfolio Optimization (PDF) - Pafka, Potters, and Kondor

Noise Dressing of Financial Correlation Matrices (PDF) - Laloux, Cizeau, Bouchaud, and Potters

Random Matrix Theory and Financial Correlations (PDF) - Laloux, Cizeau, Bouchaud, and Potters

Rational Decisions, Random Matrices and Spin Glasses (PDF) - Galluccio, Bouchaud, and Potters

Random Matrices and the Replica Method

Principal Component Analysis Eigenvalue Spectra from Data with Symmetry Breaking Structure (PDF) - Hoyle and Rattray