A Limit Theorem for Scaled Eigenvectors of Random Dot Product Graphs

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Limit theorems for eigenvectors of the normalized Laplacian for random graphs (2016, background): “More specifically, the limit result in [4] states that, for stochastic blockmodel graphs, conditional on the block assignments the entries of the scaled eigenvectors corresponding to the few largest eigenvalues of the adjacency matrix converge to a multivariate normal (see Theorem 2.”
Statistical Inference on Random Dot Product Graphs: a Survey (2017, methodology): “The classic results of Füredi and Komlós [39] describe the eigenvalues of the Erdős-Rényi random graph and the work of Tao and Vu [102] is focused on distributions of eigenvectors of more general random matrices under moment restrictions, but [8] and [98] are among the only references for central li”