Universality of extremal eigenvalues of large non-Hermitian random matrices
数学专题报告
报告题目(Title)：Universality of extremal eigenvalues of large non-Hermitian random matrices
报告人(Speaker)：许媛媛(中科院)
地点(Place)：后主楼1124
时间(Time)：2024年4月22日(周一)下午2:00-4:00
邀请人(Inviter)：陈昕昕
报告摘要
We will report recent progress on the universality of extremal eigenvalues of a large random matrix with i.i.d. entries. Beyond the radius of the celebrated circular law, we will establish a precise three-term asymptotic expansion for the largest eigenvalue (in modulus) with an optimal error term. Based on this result, we will further show that the properly normalized largest eigenvalue converges to a Gumbel distribution as the dimension goes to infinity. Furthermore, we also prove that the argument of the largest eigenvalue is uniform on the unit circle and that the extremal eigenvalues form a Poisson point process. Similar results also apply to the rightmost eigenvalues. These results are based on several joint works with Giorgio Cipolloni, Laszlo Erdos, and Dominik Schroder.
