Mathematics

After a general introduction to the universality of local eigenvalue statistics for random matrices, I discuss results on local eigenvalue statistics for random regular graphs. Under mild growth assumptions on the degree, we prove that the local semicircle law holds at the optimal scale, and that the bulk eigenvalue statistics ​coincide with those of​ ​the​ GOE​ from random matrix theory​. Joint work with ​R. Bauerschmidt, ​J. Huang, and H.-T. Yau.