On correlation function of high moments of large Wigner random matrices

DOI10.1515/ROSE-2013-0016zbMATH Open1281.15043arXiv1011.3965OpenAlexW2964057849MaRDI QIDQ2873157

Oleksiy Khorunzhiy

Publication date: 23 January 2014

Published in: Random Operators and Stochastic Equations (Search for Journal in Brave)

Abstract: 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).

Full work available at URL: https://arxiv.org/abs/1011.3965

zbMATH Keywords

eigenvalue distributionrandom matricesWigner ensembleinverse participation ratioGaussian unitary invariant ensemble

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

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High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices ⋮ High moments of large Wigner random matrices and asymptotic properties of the spectral norm

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