We solve the problem on local statistics of finite Lyapunov exponents for M products of N×N Gaussian random matrices as both M and N go to infinity, proposed by Akemann, Burda, Kieburg and Deift. When the ratio (M+1)/N changes from 0 to ∞, we prove that the local statistics undergoes a transition from GUE to Gaussian. Especially at the critical scaling (M+1)/N → γ ∈ (0,∞), we observe a phase transition phenomenon.
Dang-Zheng Liu is an Associate Professor at University of Science and Technology of China. He received Ph.D. degree in Mathematics from Peking University. His research interest is in random matrix theory, particularly, in products of random matrices.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai