Title: Emergence of a spectral gap in a class of random matrices associated with split graphs,
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.