• Corpus ID: 247292842

Entrywise limit theorems of eigenvectors for signal-plus-noise matrix models with weak signals

@inproceedings{Xie2021EntrywiseLT,
  title={Entrywise limit theorems of eigenvectors for signal-plus-noise matrix models with weak signals},
  author={Fangzheng Xie},
  year={2021}
}
We establish a finite-sample Berry-Esseen theorem for the entrywise limits of the eigenvectors for a broad collection of signal-plus-noise random matrix models under challenging weak signal regimes. The signal strength is characterized by a scaling factor $\rho_n$ through $n\rho_n$, where $n$ is the dimension of the random matrix, and we allow $n\rho_n$ to grow at the rate of $\log n$. The key technical contribution is a sharp finite-sample entrywise eigenvector perturbation bound. The existing… 

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