Abstract：

We will report on recent progress regarding the universality of the extreme 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. Similar results also apply to the rightmost eigenvalue of the matrix. These results are based on several joint works with Giorgio Cipolloni, Laszlo Erdos, and Dominik Schroder.

About the Speaker:

Yuanyuan Xu 许媛媛

Academy of Mathematics and Systems Science

Chinese Academy of Sciences

I am interested in probability theory, mathematical physics, and high-dimensional statistics, with a focus on random matrix theory.

I am currently a tenure-track assistant professor at Academy of Mathematics and Systems Science, Chinese Academy of Sciences (AMSS, CAS).

Before that, I was a postdoc in the group of László Erdős at Institute of Science and Technology Austria (IST Austria) from 2021-2023. During 2018-2021, I was a postdoc at KTH Royal Institute of Technology, working with Kevin Schnelli. I obtained my Ph.D. degree in applied mathematics from University of California, Davis in 2018, under the supervision of Alexander Soshnikov. I received my B.S. degree in applied mathematics from University of Science and Technology of China (USTC) in 2013.