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

Sean O’Rourke (), David Renfrew () and Alexander Soshnikov ()
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Sean O’Rourke: University of California, Davis
David Renfrew: University of California, Davis
Alexander Soshnikov: University of California, Davis

Journal of Theoretical Probability, 2013, vol. 26, issue 3, 750-780

Abstract: 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

Keywords: Wigner; random; matrices; 15A52 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-011-0396-x

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