Products of large random matrices
[TMCSC]
Sep 22-Dec 08, 2020
每周二，14:00-16:00
腾讯会议（线上）
ID: 742 1651 4752 Password: 235711
SPEAKER
刘党政（中国科学技术大学）
ABSTRACT
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..
SUPPORTED BY
国家天元数学西南中心
四川大学数学学院