Level: |
BSc, MSci, MSc |
Title: |
Random matrices |
Supervisor: |
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Research Area: |
Probability and Applications [Including Statistics] |
Description: |
A random matrix is a matrix which has random entries. A key aim of random matrix theory is establishing deterministic properties of eigenvalues as the dimension of the matrix gets large. The starting point of this project will be to understand the Wigner semicircle law and to obtain numerical verification. Possible further extensions include an analysis of heavy tailed random matrices, random covariance matrices, and Dyson Brownian motion.
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Further Reading: |
- G. W. Anderson, A. Guionnet, O. Zeitouni, An Introduction to Random Matrices. Cambridge studies in advanced mathematics, Vol. 118, Cambridge Univ. Press, Cambridge, 2010 [http://cims.nyu.edu/~zeitouni/cupbook.pdf].
- T. Tao, Topics in Random Matrix Theory. Graduate Studies in Mathematics, Vol. 132, American Mathematical Society, 2012 [https://terrytao.files.wordpress.com/2011/02/matrix-book.pdf].
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Key Modules: |
To be confirmed with the supervisor.
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Other Information: |
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Current Availability: |
Yes |
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