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- W3208294655 abstract "We derive the limiting distribution for the outlier eigenvalues of the adjacency matrix for random graphs with independent edges whose edge probability matrices have low-rank structure. We show that when the number of vertices tends to infinity, the leading eigenvalues in magnitude are jointly multivariate Gaussian with bounded covariances. As a special case, this implies a limiting normal distribution for the outlier eigenvalues of stochastic blockmodel graphs and their degree-corrected or mixed-membership variants. Our result extends the classical result of Füredi and Komlós on the fluctuation of the largest eigenvalue for Erdős–Rényi graphs." @default.
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- W3208294655 date "2021-11-03" @default.
- W3208294655 modified "2023-09-26" @default.
- W3208294655 title "Eigenvalues of Stochastic Blockmodel Graphs and Random Graphs with Low-Rank Edge Probability Matrices" @default.
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- W3208294655 doi "https://doi.org/10.1007/s13171-021-00268-x" @default.
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