Bulk eigenvalue statistics for random regular graphs

Abstract

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.

References in corpus (6)

• Bulk universality of sparse random matrices
• Local semicircle law for random regular graphs
• Fixed energy universality for generalized Wigner matrices
• Spectral statistics of sparse Erdős-Rényi graph Laplacians
• Universality of random matrices with correlated entries
• Dyson's Brownian-motion model for random matrix theory - revisited. With an Appendix by Don Zagier

Cited by in corpus (22)

• Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals
• Local Kesten--McKay law for random regular graphs
• Stability of the Matrix Dyson Equation and Random Matrices with Correlations
• Size biased couplings and the spectral gap for random regular graphs
• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Edge rigidity and universality of random regular graphs of intermediate degree
• Local spectral statistics of Gaussian matrices with correlated entries
• A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition
• Moments of the inverse participation ratio for the Laplacian on finite regular graphs
• Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
• Delocalization and continuous spectrum for ultrametric random operators
• On the second eigenvalue of random bipartite biregular graphs
• The spectral gap of dense random regular graphs
• Universality of random matrices with correlated entries
• Spectral gap and edge universality of dense random regular graphs
• A supersymmetric hierarchical model for weakly disordered $3d$ semimetals
• Local Marchenko-Pastur Law for Random Bipartite Graphs
• Bulk Universality for Generalized Wigner Matrices With Few Moments
• Bulk Eigenvalue Correlation Statistics of Random Biregular Bipartite Graphs
• Local Correlation and Gap Statistics under Dyson Brownian Motion for Covariance Matrices
• A Local Law for Singular Values from Diophantine Equations
• Eigenvectors of the square grid plus GUE