# 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}
}
• Published 9 April 2011
• Mathematics
• Journal of Theoretical Probability
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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