Seminar| Institute of Mathematical Sciences
Time：Friday, May 26th, 2023, 15:00-16:00
Speaker: 何煜坤(Yukun He), 香港城市大学(City University of Hong Kong)
Abstract: Let A be the adjacency matrix of a random d-regular graph on N vertices. For N^(2/3)≪d≤N/2, we prove optimal rigidity estimates of the extreme eigenvalues of A, which in particular imply that the graph is Ramanujian with very high probability. In the same regime of d, we also show that the extreme eigenvalues have Tracy-Widom fluctuations.