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arXiv · 1609.01873

Wigner law for matrices with dependent entries - a perturbative approach

T. Krajewski·A. Tanasa·D. L. Vu
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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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T. Krajewski, A. Tanasa, D. L. Vu. 2016-09-07. Wigner law for matrices with dependent entries - a perturbative approach. https://doi.org/10.1088/1751-8121%2Faa64ae

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