MATH-GA.2420-004 Advanced Topics: Universality In Random Matrix Theory (1st Half Of Semester)

1.5 points

Course Description

In these seven courses, we will first introduce the classical Gaussian Hermitian ensembles and calculate their local spectral statistics. The main goal for this class will then be to present a self-contained proof of universality of these statistics for Wigner matrices, through:

  1. estimates on the resolvent up to small scales; 
  2. distribution of the eigenvalues;
  3. distribution of the eigenvectors.

The Dyson Brownian motion will play a key role.

Prerequisites

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Sample Exams

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