Emergence of a spectral gap in a class of random matrices associated with split graphs
Physics and Society
2017-12-08 v1 Statistical Mechanics
Spectral Theory
Adaptation and Self-Organizing Systems
Abstract
Motivated by the intriguing behavior displayed in a dynamic network that models a population of extreme introverts and extroverts (XIE), we consider the spectral properties of ensembles of random split graph adjacency matrices. We discover that, in general, a gap emerges in the bulk spectrum between -1 and 0 that contains a single eigenvalue. An analytic expression for the bulk distribution is derived and verified with numerical analysis. We also examine their relation to chiral ensembles, which are associated with bipartite graphs.
Cite
@article{arxiv.1712.02429,
title = {Emergence of a spectral gap in a class of random matrices associated with split graphs},
author = {Kevin E. Bassler and R. K. P. Zia},
journal= {arXiv preprint arXiv:1712.02429},
year = {2017}
}
Comments
17 pages, 6 figures