Sparse random matrices: spectral edge and statistics of rooted trees

By A. Khorunzhy. Advances in Applied Probability, 2001

54 citations recorded by the source corpus.

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OSNAP: Faster Numerical Linear Algebra Algorithms via Sparser Subspace Embeddings (2012, unknown): “[28, 29, 50]).”
Sparse regular random graphs: Spectral density and eigenvectors (2009, background): “y d-regular graph and we cite it from Friedman [29]: |λ 2|≥2 √ d−1+ O(logd/logn). Unfortunately, when dgrows with n, the upper bound is not known to hold outside of a narrow growth regime.3 Khorunzhy [37] has shown that, for a random matrix model similar to the adjacency matrix of the Erd˝os–Reny´i ”
Transition from Tracy–Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs (2017, background): “It was proven in [38], that the spectral norm converges to 2 if and only if p logN .”
Spectral norm of products of random and deterministic matrices (2008, methodology): “The spectral norm of random sparse matrices was studied in [16] as a development of the work of Z.”
Angular Synchronization by Eigenvectors and Semidefinite Programming (2009, unknown): “The spectral norm of such sparse random matrices was studied in [25,24] where it was shown that with probability 1,”