  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 $N\times N$
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 $k\gg
N^{5/3}$, then $v^{[k]}$ is almost orthogonal to $v$.

Probability