Special software is required to use some of the files in this section: .ps.
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:
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 ProjectsTOPICS | RELATED PAPERS |
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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 |
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 Regular Spacings of Complex Eigenvalues in the One-Dimensional Non-Hermitian Anderson Model - 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 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 - 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 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 Law of Addition in Random Matrix Theory - Zee |
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. RNA Folding and Large N Matrix Theory - Zee |
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 Random Matrices, Free Probability and the Replica Method (PS) - Mueller |