# Noise sensitivity for the top eigenvector of a sparse random matrix

@inproceedings{Bordenave2021NoiseSF, title={Noise sensitivity for the top eigenvector of a sparse random matrix}, author={Charles Bordenave and Jaehun Lee}, year={2021} }

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…

## 2 Citations

### Higher order fluctuations of extremal eigenvalues of sparse random matrices

- Mathematics
- 2021

We consider extremal eigenvalues of sparse random matrices, a class of random matrices including the adjacency matrices of Erdős-Rényi graphs G(N, p). Recently, it was shown that the leading order…

### Resampling Sensitivity of High-Dimensional PCA

- Mathematics
- 2022

It is shown that PCA is sensitive to the input data in the sense that resampling even a negligible portion of the input may completely change the output.

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