Publication: Fluctuations of extreme eigenvalues of sparse Erdős–Rényi graphs
Fluctuations of extreme eigenvalues of sparse Erdős–Rényi graphs
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He, Y., & Knowles, A. (2021). Fluctuations of extreme eigenvalues of sparse Erdős–Rényi graphs. Probability Theory and Related Fields, 180, 985–1056. https://doi.org/10.1007/s00440-021-01054-4
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We consider a class of sparse random matrices which includes the adjacency matrix of the Erdős-Rényi graph G(N,p) . We show that if Nε⩽Np⩽N1/3−ε then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. This extends the result (Huang et al. in Ann Prob 48:916-962, 2020) on the fluctuations of the extreme eigenvalues from Np⩾N2/9+ε down to the optimal scale Np⩾Nε . The main technical a
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- He, Yukun
- Knowles, Antti
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He, Y., & Knowles, A. (2021). Fluctuations of extreme eigenvalues of sparse Erdős–Rényi graphs. Probability Theory and Related Fields, 180, 985–1056. https://doi.org/10.1007/s00440-021-01054-4
