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 ≫ 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.

Locations

• Journal of Mathematical Physics - View
• arXiv (Cornell University) - View - PDF
• Digital Access to Scholarship at Harvard (DASH) (Harvard University) - View - PDF
• DataCite API - View