Bulk universality of sparse random matrices

Abstract

We consider the adjacency matrix of the ensemble of Erdős-Rényi random graphs which consists of graphs on $N$ vertices in which each edge occurs independently with probability $p$. We prove that in the regime $pN\gg 1$ these matrices exhibit bulk universality in the sense that both the averaged $n$-point correlation functions and distribution of a single eigenvalue gap coincide with those of the GOE. Our methods extend to a class of random matrices which includes sparse ensembles whose entries have different variances.

20 pages

References in corpus (4)

• Spectra of Sparse Random Matrices
• Fixed energy universality for generalized Wigner matrices
• Spectral Statistics of Sparse Random Graphs with a General Degree Distribution
• Random matrices: tail bounds for gaps between eigenvalues

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