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This is proven at the spectrum's edge and for slowly growing d, but not in the bulk at fixed d.","posed_since":"","precise":"Adjacency matrix of a uniform random d-regular graph on $N$ vertices with $d\\ge 3$ fixed. Prove that bulk local eigenvalue statistics (e.g. the gap distribution at a fixed energy inside $(-2\\sqrt{d-1}, 2\\sqrt{d-1})$) converge to GOE as $N\\to\\infty$. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof of GOE bulk gap or correlation universality for one fixed d.","status_note":"Bulk universality is proven for $N^{\\alpha} \\le d \\le N^{2/3-\\alpha}$ (Bauerschmidt, Huang, Knowles and Yau, Annals of Probability 2017, arXiv 1505.06700); at fixed d, optimal eigenvalue rigidity and Tracy-Widom edge universality were proven by Huang, McKenzie and Yau (arXiv 2412.20263, 2024).","title":"Random-matrix bulk statistics for random regular graphs of fixed 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