Local eigenvalue statistics for random regular graphs

Local eigenvalue statistics for random regular graphs - Bauerschmidt

Roland Bauerschmidt
Harvard University
March 16, 2016
I will discuss results on local eigenvalue statistics for uniform random regular graphs. For graphs whose degrees grow slowly with the number of vertices, we prove that the local semicircle law holds at the optimal scale, and that the bulk eigenvalue statistics (gap statistics and averaged energy correlation functions) are given by those of the GOE. This is joint work with J. Huang, A. Knowles, and H.-T. Yau.