Wigner law for matrices with dependent entries - a perturbative approach
arXiv:1609.01873 · doi:10.1088/1751-8121/aa64ae
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.
9 pages, 4 figures