@article{5143f142e1b04f1ba38582af9a05b0ea, title = "Bulk eigenvalue fluctuations of sparse random matrices", abstract = "We consider a class of sparse random matrices, which includes the adjacency matrix of Erd{\H o}s–R{\'e}nyi graphs G(N, p) for p ∈ [Nϵ-1, N-ϵ]. We identify the joint limiting distributions of the eigenvalues away from 0 and the spectral edges. Our result indicates that unlike Wigner matrices, the eigenvalues of sparse matrices satisfy central limit theorems with normalization N√p. In addition, the eigenvalues fluctuate simultaneously: the correlation of two eigenvalues of the same/different sign is asymptotically 1/-1. We also prove CLTs for the eigenvalue counting function and trace of the resolvent at mesoscopic scales.", keywords = "CLT, random matrices, sparse Erd{\H o}s–R{\'e}nyi graphs", author = "Yukun HE", year = "2020", month = dec, doi = "10.1214/20-AAP1575", language = "English", volume = "30", pages = "2846--2879", journal = "Annals of Applied Probability", issn = "1050-5164", publisher = "Institute of Mathematical Statistics", number = "6", }