Emergence of a spectral gap in a class of random matrices associated with split graphs. (5th December 2017) - Bassler, Kevin E; Zia, R K P
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.