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We show that Wigner semi-circle law holds for Hermitian matrices withdependent entries, provided the deviation of the cumulants from the normalisedGaussian case obeys a simple power law bound in the size of the matrix. Toestablish this result, we use replicas interpreted as a zero-dimensionalquantum field theoretical model whose effective potential obey arenormalisation group equation.

Wigner law for matrices with dependent entries - a perturbative approach