Phase transitions for infinite products of large non-Hermitian random matrices

Abstract: Products of M i.i.d. random matrices of size N relate classical limit theorems in Probability Theory (large M and N=1) to Lyapunov exponents in Dynamical Systems (large M and finite N), and to universality in Random Matrix Theory (finite M and large N). Under the two different limits of large M and large N, the eigenvalue statistics for the random matrix product display Gaussian and non-Hermitian RMT universality, respectively. However, what happens if both M and N go to infinity simultaneously? This problem lies at the heart of understanding two kinds of universal limits. In this talk we examine it and investigate possible phase transitions and critical phenomena.

Mathematics

Audience: researchers in the topic

ICCM 2020