Emergence of a spectral gap in a class of random matrices associated with split graphs. (5th December 2017)

• Record Type: Journal Article
• Authors: Bassler, Kevin E; Zia, R K P
• Is Part Of: Journal of physics. Volume 51:Number 1(2018)
• Publication Date: 2017-12-05
• Subjects: spectral gap -- random matrices -- extreme introverts and extroverts (XIE) -- split graphs -- bipartite graphs; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa94a9
• Languages: English
• ISSNs: 1751-8113

Abstract

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.