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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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)…
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Non-Gaussian Limiting Laws for the Entries of Regular Functions of the Wigner Matrices
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