Spectral statistics of the uni-modular ensemble
Mathematical Physics
2017-09-13 v1 Disordered Systems and Neural Networks
Statistical Mechanics
math.MP
Probability
Abstract
We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U (1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a supersymmetric integration method, a combinatorial graph-theoretical analysis and a Brownian motion approach, we are able to derive expressions for 1/N corrections to the mean spectral moments and also analyse the fluctuations about this mean. By addressing the same ensemble from three different point of view, we can critically compare their relative advantages and derive some new results.
Cite
@article{arxiv.1703.09587,
title = {Spectral statistics of the uni-modular ensemble},
author = {Christopher H. Joyner and Uzy Smilansky and Hans A. Weidenmüller},
journal= {arXiv preprint arXiv:1703.09587},
year = {2017}
}
Comments
35 pages, 3 figures