Optimal delocalization for generalized Wigner matrices

  title={Optimal delocalization for generalized Wigner matrices},
  author={Lucas Benigni and Patrick Lopatto},
  journal={Advances in Mathematics},
We study the eigenvectors of generalized Wigner matrices with subexponential entries and prove that they delocalize at the optimal rate with overwhelming probability. We also prove high probability delocalization bounds with sharp constants. Our proof uses an analysis of the eigenvector moment flow introduced by Bourgade and Yau (2017) to bound logarithmic moments of eigenvector entries for random matrices with small Gaussian components. We then extend this control to all generalized Wigner… 

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