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Introduction to Random Matrices

Instructor: Laszlo Erdös

Teaching Assistant: Torben Krueger



Random matrices were first introduced in statistics in the 1920's, but they were made famous by Eugene Wigner's revolutionary vision. He predicted that spectral lines of heavy nuclei can be modelled by the eigenvalues of random symmetric matrices with independent entries (Wigner matrices). In particular, he conjectured that the statistics of energy gaps is given by a universal distribution that is independent of the detailed physical parameters. While the proof of this conjecture for realistic physical models is still beyond reach, it has recently been shown that the gap statistics of Wigner matrices is independent of the distribution of the matrix elements. Students will be introduced to the fascinating world of random matrices and presented with some of the basic tools for their mathematical analysis in this course. 

pre-requisites: basic linear algebra and probability theory would help but are not required . 
Target audience: maths/ physics/ CS students


There will be an oral exam at the end of the course.





Final Grade

The final grade is determined by the oral exam.







Schedule (subject to change)

Lectures: Tuesday/Thursday 10:15-11:30, Mondi 2

Recitation: Tuesday, 11:30-12:15, Mondi 2


Short content of the lectures:




File Due Date

Additional Downloads

 Tucson Lecture Notes Pedagogical lecture notes about basic theory of random matrices


CDM Lecture Notes Lecture notes about the latest developments


Slides Some slides with pictures