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- W4320196239 abstract "Let $G=G(n,p_n)$ be a homogeneous Erdos-R'enyi graph, $A$ its adjacency matrix with eigenvalues $lambda_1(A) geq lambda_2(A) geq ... geq lambda_n(A).$ In such cases, it has been shown using local laws that $lambda_2(A)$ can exhibit different behaviors: real-valued Tracy-Widom for $p_n gg n^{-2/3},$ normal for $n^{-7/9} ll p_n ll n^{-2/3},$ or a mix of the two for $p_n=cn^{-2/3}.$ Additionally, this technique renders the largest eigenvalue $lambda_1(A),$ separated from the rest of the spectrum for $p_n gg n^{-1},$ has Gaussian fluctuations when $p_n gg n^{-1/3}.$ This paper extends the range of the last convergence to $n^{epsilon-1} leq p_n leq frac{1}{2}, epsilon in (0,1):$ the tool behind this is a CLT for the eigenvalue statistics of $A,$ which is justified by the method of moments." @default.
- W4320196239 created "2023-02-13" @default.
- W4320196239 creator A5069138969 @default.
- W4320196239 date "2022-10-18" @default.
- W4320196239 modified "2023-09-26" @default.
- W4320196239 title "Two CLTs for Sparse Random Matrices" @default.
- W4320196239 doi "https://doi.org/10.48550/arxiv.2210.09625" @default.
- W4320196239 hasPublicationYear "2022" @default.
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