Universality of the Local Eigenvalue Statistics for a Class of Unitary Invariant Random Matrix Ensembles
نویسندگان
چکیده
The paper is devoted to the rigorous proof of the universality conjecture of the random matrix theory, according to which the limiting eigenvalue statistics of n n random matrices within spectral intervals of the order O(n ) is determined by the type of matrices (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 arose in the quantum eld theory and have the unitary invariant distribution de ned by a certain function (the potential in the quantum eld theory) satisfying some regularity conditions.
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