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We show that if the non-Gaussian part of the cumulants of a random matrix model obeys some scaling bounds in the size of the matrix, then Wigner’s semicircle law holds. This result is derived using the replica technique and an analogue of the renormalisation group equation for the replica effective action.

A Renormalisation Group Approach to the Universality of Wigner’s Semicircle Law for Random Matrices with Dependent Entries