On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-Identically Distributed Entries
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 \ ∫ (1+|k|)2s\*|f(k)|2 \* dk <∞.
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