English

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

Probability 2014-08-18 v4 Mathematical Physics math.MP

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<.s>3 \ \int (1+|k|)^{2s}\*|\hat{f}(k)|^2 \* dk <\infty.

Keywords

Cite

@article{arxiv.1104.1663,
  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= {arXiv preprint arXiv:1104.1663},
  year   = {2014}
}

Comments

accepted for publication in Journal of Theoretical Probability