讲座题目：Phase transition of eigenvalues in deformed Ginibre ensembles

讲座人：张禄  中国科学技术大学

讲座时间：2022年5月15号上午09:30

讲座地点： 腾讯会议,  3428925924,  密码: 123456

主办单位：数学与统计学院

欢迎光临

报告摘要：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.

报告人简介：Lu Zhang, School of Mathematical Sciences, student of University of Science and Technology of China, Hefei 230026, P.R. China.