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- W2920794489 abstract "We investigate the noise sensitivity of the top eigenvector of a Wigner matrix in the following sense. Let $v$ be the top eigenvector of an $Ntimes N$ Wigner matrix. Suppose that $k$ randomly chosen entries of the matrix are resampled, resulting in another realization of the Wigner matrix with top eigenvector $v^{[k]}$. We prove that, with high probability, when $k ll N^{5/3-o(1)}$, then $v$ and $v^{[k]}$ are almost collinear and when $kgg N^{5/3}$, then $v^{[k]}$ is almost orthogonal to $v$." @default.
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- W2920794489 date "2019-03-12" @default.
- W2920794489 modified "2023-10-18" @default.
- W2920794489 title "Noise sensitivity of the top eigenvector of a Wigner matrix" @default.
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