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

Author

Listed:
  • Sean O’Rourke

    (University of California, Davis)

  • David Renfrew

    (University of California, Davis)

  • Alexander Soshnikov

    (University of California, Davis)

Abstract

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

Suggested Citation

  • Sean O’Rourke & David Renfrew & Alexander Soshnikov, 2013. "On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-identically Distributed Entries," Journal of Theoretical Probability, Springer, vol. 26(3), pages 750-780, September.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:3:d:10.1007_s10959-011-0396-x
    DOI: 10.1007/s10959-011-0396-x
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    Cited by:

    1. Jan Nagel, 2021. "A Functional CLT for Partial Traces of Random Matrices," Journal of Theoretical Probability, Springer, vol. 34(2), pages 953-974, June.
    2. Dörnemann, Nina & Dette, Holger, 2023. "Fluctuations of the diagonal entries of a large sample precision matrix," Statistics & Probability Letters, Elsevier, vol. 198(C).

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    Keywords

    Wigner random matrices;

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