Level crossing in random matrices. II Random perturbation of a random matrix
Mathematical Physics
2019-05-22 v2 High Energy Physics - Theory
math.MP
Abstract
In this paper we study the distribution of level crossings for the spectra of linear families A+lambda B, where A and B are square matrices independently chosen from some given Gaussian ensemble and lambda is a complex-valued parameter. We formulate a number of theoretical and numerical results for the classical Gaussian ensembles and some generalisations. Besides, we present intriguing numerical information about the distribution of monodromy in case of linear families for the classical Gaussian ensembles of 3 * 3 matrices.
Keywords
Cite
@article{arxiv.1806.08732,
title = {Level crossing in random matrices. II Random perturbation of a random matrix},
author = {Tobias Grøsfjeld and Boris Shapiro and Konstantin Zarembo},
journal= {arXiv preprint arXiv:1806.08732},
year = {2019}
}
Comments
27 pages, many figures