Seminar Analysis: Antti Knowles (ETH Zürich)

Local eigenvalue statistics for random regular graphs

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.)

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