|DATE||November 17 (Wed), 2021|
|INSTITUTE||Korea Advanced Institute of Science and Technology|
|TITLE||[GS_M_APP] Tracy-Widom limit for free sum of random matrices|
|ABSTRACT||In random matrix theory, local statistics of the eigenvalues of random matrices have been studied extensively. Among the flourishing researches, one of the most remarkable concepts in random matrix theory is the universality phenomenon. The universality implies that the local eigenvalue statistics depend only on the symmetric class of the matrix ensembles.
In this talk, I will explain the Tracy-Widom limit for the largest eigenvalue of the sum of two unitarily invariant matrices establishing the edge universality of the free sum of random matrices.
The proof is based on the Green function comparison method and local statistics of Dyson Brownian motion, a continuous flow of random matrix, starting from the original matrix. I will also explain the free additive convolution of probability measures, analytic subordination system of the convolution and its stability.
This talk is based on a joint work with Hong Chang Ji.