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- W3198280605 abstract "We analyse the eigenvectors of the adjacency matrix of the Erdős-Renyi graph on $N$ vertices with edge probability $frac{d}{N}$. We determine the full region of delocalization by determining the critical values of $frac{d}{log N}$ down to which delocalization persists: for $frac{d}{log N} > frac{1}{log 4 - 1}$ all eigenvectors are completely delocalized, and for $frac{d}{log N} > 1$ all eigenvectors with eigenvalues away from the spectral edges are completely delocalized. Below these critical values, it is known [arXiv:2005.14180, arXiv:2106.12519] that localized eigenvectors exist in the corresponding spectral regions." @default.
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- W3198280605 date "2021-09-07" @default.
- W3198280605 modified "2023-09-27" @default.
- W3198280605 title "The completely delocalized region of the ErdH{o}s-R'enyi graph" @default.
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