On correlation function of high moments of Wigner random matrices

Details On correlation function of high moments of Wigner random matrices On correlation function of high moments of Wigner random matrices

2010-11-17

arxiv.org/abs/1011.3965v2

Physics

Mathematical Physics

Version 2: denotations of (4.2) and other misprints corrected; minor changes at the end of Section 3

Scientific paper

We consider the Wigner ensemble of Hermitian n-dimensional random matrices and study the correlation function K(s',s") of their moments in the limit when the numbers s', s" of the moments are proportional to n to the power 2/3. We show that the limiting expression of K does not depend on the moments of the random matrix elements. The proof is based on a combination of the arguments by Ya. Sinai and A. Soshnikov with the detailed study of a moment analog of the Inverse Participation Ratio of the Gaussian Unitary Invariant Ensemble (GUE).

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