Local eigenvalue statistics for random regular graphs

Local eigenvalue statistics for random regular graphs

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Roland Bauerschmidt , Harvard University
Jadwin Hall 343

I will discuss results on local eigenvalue statistics for uniform 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 (gap statistics and averaged energy correlation functions) are given by those of the GOE. Joint work with J. Huang, A. Knowles, and H.-T. Yau.