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Advances in High Energy Physics
Volume 2017 (2017), Article ID 4098720, 7 pages
https://doi.org/10.1155/2017/4098720
Research Article

A Renormalisation Group Approach to the Universality of Wigner’s Semicircle Law for Random Matrices with Dependent Entries

Centre de Physique Théorique, Aix-Marseille Université, Marseille, France

Correspondence should be addressed to Thomas Krajewski

Received 15 June 2017; Revised 1 September 2017; Accepted 1 October 2017; Published 31 December 2017

Academic Editor: Ralf Hofmann

Copyright © 2017 Thomas Krajewski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

We show that if the non-Gaussian part of the cumulants of a random matrix model obeys some scaling bounds in the size of the matrix, then Wigner’s semicircle law holds. This result is derived using the replica technique and an analogue of the renormalisation group equation for the replica effective action.