Corpus ID: 210156949

Noise sensitivity of second-top eigenvectors of Erd\H{o}s-R\'{e}nyi graphs and sparse matrices

@article{Lee2020NoiseSO,
  title={Noise sensitivity of second-top eigenvectors of Erd\H\{o\}s-R\'\{e\}nyi graphs and sparse matrices},
  author={Jaehun Lee},
  journal={arXiv: Probability},
  year={2020}
}
  • Jaehun Lee
  • Published 2020
  • Mathematics
  • arXiv: Probability
We consider eigenvectors of adjacency matrices of Erd\H{o}s-R\'{e}nyi graphs and study the variation of their directions by resampling the entries randomly. Let $\mathbf{v}$ be the eigenvector associated with the second-largest eigenvalue of the Erd\H{o}s-R\'{e}nyi graphs. After choosing $k$ entries of the given matrix randomly and resampling them, we obtain another eigenvector $\mathbf{w}$ corresponding to the second-largest eigenvalue of the matrix obtained from the resampling procedure. We… Expand

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