Lyapunov exponent,universality and phase transition for products of random matrices

Title: Lyapunov exponent,universality and phase transition   for  products of random matrices

Speaker: Dr. 刘党政 ,  中国科技大学

Time:  2:00pm, 2018-12-21

Location:  200-9, Sir R.R.Shaw Building, Yuquan Campus, Zhejiang University

Abstract: We solve the problem on local statistics of finite Lyapunov exponents for M products of  NXN 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  infinity , we prove that the local statistics undergoes a transition from GUE to Gaussian. Especially at the critical scaling  (M+1)/N /to /gamma /in (0,/infty)， we observe a phase transition phenomenon.

Contact Person: Zhonggen Su,  suzhonggen@zju.edu.cn