On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-identically Distributed Entries

@article{ORourke2011OnFO,
  title={On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-identically Distributed Entries},
  author={Sean O’Rourke and David Renfrew and Alexander Soshnikov},
  journal={Journal of Theoretical Probability},
  year={2011},
  volume={26},
  pages={750-780}
}
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 non-i.i.d. entries provided certain Lindeberg type conditions for the fourth moments are satisfied. In addition, we relax our conditions on the test functions and require that for some s>3 $$\int_{\mathbb{R}} \bigl(1+ 2|k|\bigr)^{2s} \bigl|\hat{f}(k)\bigr|^2 \,dk <\infty.$$ 
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