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- W3113209803 abstract "We consider a class of sparse random matrices, which includes the adjacency matrix of Erdős–Rényi graphs $mathcal{G}(N,p)$ for $pin [N^{varepsilon -1},N^{-varepsilon }]$. 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 $Nsqrt{p}$. 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." @default.
- W3113209803 created "2020-12-21" @default.
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- W3113209803 date "2020-12-01" @default.
- W3113209803 modified "2023-09-27" @default.
- W3113209803 title "Bulk eigenvalue fluctuations of sparse random matrices" @default.
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- W3113209803 doi "https://doi.org/10.1214/20-aap1575" @default.
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