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) |