Work

Bulk eigenvalue statistics for random regular graphs

Year: 2017

Type: article

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.

Source: The Annals of Probability

DOI: 10.1214/16-aop1145

Authors: Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles, Horng-Tzer Yau

Institutions: Harvard University, University of Cambridge, University of Geneva, ETH Zurich

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Awards: Spectral and eigenvector statistics of large random matrices, Random Matrices and Disordered Systems