Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices

@article{Pizzo2011FluctuationsOM,
  title={Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices},
  author={Alessandro Del Pizzo and David Renfrew and Alexander Soshnikov},
  journal={Journal of Statistical Physics},
  year={2011},
  volume={146},
  pages={550-591}
}
We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A. Lytova and L. Pastur (J. Stat. Phys. 134:147–159, 2009). Our results are valid provided the off-diagonal matrix entries have finite fourth moment, the diagonal matrix entries have finite second moment, and the test functions have four continuous derivatives in a… 
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In this note, we extend the results about the fluctuations of the matrix entries of regular functions of Wigner random matrices obtained in Pizzo et al. (arXiv:1103.1170) to Wigner matrices with
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