报 告 题 目：Phase transition of eigenvalues  in deformed Ginibre ensembles

主 讲 人：张 禄

单 位：中国科学技术大学

时 间：5月15日9:30

腾讯 ID：342-892-5924

密 码：123456

摘 要：

Consider a random matrix of size N as an additive deformation of the complex Ginibre ensemble under a deterministic matrix X0 with a finite rank, independent of  N. When some eigenvalues of X0 separate from the unit disk, outlier eigenvalues may appear asymptotically in the same locations, and their fluctuations exhibit surprising phenomena that highly depend on the Jordan canonical form of X0. These findings are largely due to Benaych-Georges and Rochet, Bordenave and Capitaine, and Tao. When all eigenvalues of X0 lie inside the unit disk, we prove that local eigenvalue statistics at the spectral edge form a new class of determinantal point processes, for which correlation kernels are characterized in terms of the repeated erfc integrals. This thus completes a non-Hermitian analogue of the BBP phase transition in Random Matrix Theory. Similar results hold for the deformed quaternion Ginibre ensemble.

简 介：

Lu Zhang, School of Mathematical Sciences, student of University of Science and Technology of China, Hefei 230026, P.R. China.