• Corpus ID: 235458169

Noise sensitivity for the top eigenvector of a sparse random matrix

  title={Noise sensitivity for the top eigenvector of a sparse random matrix},
  author={Charles Bordenave and Jaehun Lee},
We investigate the noise sensitivity of the top eigenvector of a sparse random symmetric matrix. Let v be the top eigenvector of an N × N sparse random symmetric matrix with an average of d non-zero centered entries per row. We resample k randomly chosen entries of the matrix and obtain another realization of the random matrix with top eigenvector v [ k ] . Building on recent results on sparse random matrices and a noise sensitivity analysis previously developed for Wigner matrices, we prove… 

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