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Bulk eigenvalue statistics for random regular graphs. (English) Zbl 1379.05098
Summary: We consider the uniform random \(d\)-regular graph on \(N\) vertices, with \(d\in [N^{\alpha},N^{2/3-\alpha}]\) for arbitrary \(\alpha>0\). We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian orthogonal ensemble.

MSC:
05C80 Random graphs (graph-theoretic aspects)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
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