From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective

  title={From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective},
  author={Davide Facoetti and Pierpaolo Vivo and Giulio Biroli},
  journal={arXiv: Disordered Systems and Neural Networks},
We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter $N\times N$ random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting the model as the combination of on-site random energies $\{a_i\}$ and a structurally disordered hopping, we found that each eigenstate is delocalised over $N^{2-\gamma}$ sites close in energy $|a_j-a_i|\leq N^{1-\gamma}$ in agreement with Kravtsov \emph… 

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