Abstract
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.
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Pastur, L., Shcherbina, M. Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles. J Stat Phys 86, 109–147 (1997). https://doi.org/10.1007/BF02180200
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DOI: https://doi.org/10.1007/BF02180200