Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles
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- Pastur, L. & Shcherbina, M. J Stat Phys (1997) 86: 109. doi:10.1007/BF02180200
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This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics ofn×n random matrices within spectral intervals ofO(n−1) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions.