Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices

@article{Benigni2017EigenvectorsDA,
  title={Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices},
  author={Lucas Benigni},
  journal={arXiv: Probability},
  year={2017}
}
  • L. Benigni
  • Published 19 November 2017
  • Mathematics, Physics
  • arXiv: Probability
We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\times N$ Rosenzweig-Porter model. We prove that the eigenvectors entries are asymptotically Gaussian with a specific variance, localizing them onto a small, explicit, part of the spectrum. For a well spread initial spectrum, this variance profile universally follows a heavy-tailed Cauchy distribution. The proof relies on a… 

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