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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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