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On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with
Non-Identically Distributed Entries
Published Web Location
https://arxiv.org/pdf/1104.1663.pdfNo data is associated with this publication.
Abstract
In this note, we extend the results about the fluctuations of the matrix entries of regular functions of Wigner random matrices obtained in arXiv:1103.3731 [math.PR] to Wigner matrices with non-i.i.d. entries provided certain Lindeberg type conditions for the fourth moments of the off-diagonal entries and the second moments of the diagonal entries are satisfied. In addition, we relax our conditions on the test functions and require that for some $s>3 \ \int (1+|k|)^{2s}\*|\hat{f}(k)|^2 \* dk <\infty.$