Abstract
We consider the Wigner ensemble of Hermitian n -dimensional random matrices with elements and study the asymptotic behavior of the expression in the limit such that and are the values of the order . Assuming that the random variables have a symmetric probability distribution such that all of its moments are of the sub-gaussian form, we prove that the limit of exists and does not depend on the particular values of , . 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 Green's function representation of the Inverse Participation Ratio (IPR) considered for Gaussian Unitary Invariant Ensemble of random matrices (GUE).
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