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math.PR2021
Upper tail of the spectral radius of sparse Erdős-Rényi graphs
Anirban Basak
We consider an Erdős-Rényi graph on vertices with edge probability such that \[ \sqrt{\frac{\log n}{\log \log n}} \ll np \le n^{1/2-o(1)}, \label{eq:abs}…
math.SP2021★ 3 cited
Localization of eigenvectors of non-Hermitian banded noisy Toeplitz matrices
Anirban Basak, Martin Vogel, Ofer Zeitouni
We prove localization with high probability on sets of size of order for the eigenvectors of non-Hermitian finitely banded Toeplitz matrices subject to…