涩里番

Title: Convergence rates in edge universality for Wigner matrices.

Abstract:聽Universal random matrix statistics are expected to arise in large complex correlated systems, in analogy with the ubiquity of the Gaussian distribution in systems with lots of independence. The classical Berry-Esseen CLT gives a convergence rate of of $n^{-1/2}$ to the limiting Gaussian distribution. In this talk we discuss whether an analog holds for the convergence of the largest eigenvalue of random matrices to the Tracy-Widom distribution. A key role is played by a new homogenization result at the spectral edge of Dyson Brownian motion.

Based on joint work with Tianhao Xian.