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

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\int_{\mathbb{R}} \bigl(1+ 2|k|\bigr)^{2s} \bigl|\hat{f}(k)\bigr|^2 \,dk <\infty.$$\end{document}