Wigner law for matrices with dependent entries - a perturbative approach (1609.01873v1)

Published 7 Sep 2016 in math-ph, hep-th, math.CO, and math.MP

Abstract: We show that Wigner semi-circle law holds for Hermitian matrices with dependent entries, provided the deviation of the cumulants from the normalised Gaussian case obeys a simple power law bound in the size of the matrix. To establish this result, we use replicas interpreted as a zero-dimensional quantum field theoretical model whose effective potential obey a renormalisation group equation.

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