Products of large random matrices
Sep 22-Dec 08, 2020
ID: 742 1651 4752 Password: 235711
Random Matrix Theory is at the intersection of matrix theory and probability theory, and has a wide range of applications in statistics, physics, engineering and beyond. Products of T i.i.d. random matrices of size N relate classical limit theorems in Probability Theory (large T and N=1) to Lyapunov exponents in Dynamical Systems (large T and finite N), and to universality in Random Matrix Theory (finite T and large N).
This course is divided into two major parts.
I) Introduction to random matrices in a nutshell via typical examples: Gaussian Unitary/Orthogonal Ensemble, Laguerre Unitary/Orthogonal Ensemble, real and complex Ginibre ensembles, Wigner random matrices and semicircle law.
II) Products of random matrices, including Lyapunov exponents, multiplicative ergodic theorem and phase transition from Gaussian to Tracy-Widom distributions..