Huang, JiaoyangLandon, BenjaminYau, Horng-Tzer2017-04-172015Huang, Jiaoyang, Benjamin Landon, and Horng-Tzer Yau. 2015. “Bulk Universality of Sparse Random Matrices.” Journal of Mathematical Physics 56 (12) (December): 123301. doi:10.1063/1.4936139. .0022-2488http://nrs.harvard.edu/urn-3:HUL.InstRepos:32189254We 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.en-USJournal Article2017-04-1710.1063/1.4936139