Wigner law for matrices with dependent entries - a perturbative approach
Mathematical Physics
2017-04-05 v1 High Energy Physics - Theory
Combinatorics
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.
Keywords
Cite
@article{arxiv.1609.01873,
title = {Wigner law for matrices with dependent entries - a perturbative approach},
author = {T. Krajewski and A. Tanasa and D. L. Vu},
journal= {arXiv preprint arXiv:1609.01873},
year = {2017}
}
Comments
9 pages, 4 figures