Emergence of a spectral gap in a class of random matrices associated with split graphs

Autor:	Royce K.P. Zia, Kevin E. Bassler
Rok vydání:	2017
Předmět:	Statistics and Probability Physics - Physics and Society Pure mathematics Population FOS: Physical sciences General Physics and Astronomy Physics and Society (physics.soc-ph) 01 natural sciences 010305 fluids & plasmas Mathematics - Spectral Theory Stochastic processes 0103 physical sciences FOS: Mathematics Adjacency matrix Split graph 010306 general physics education Spectral Theory (math.SP) Condensed Matter - Statistical Mechanics Mathematical Physics Eigenvalues and eigenvectors Mathematics education.field_of_study Statistical Mechanics (cond-mat.stat-mech) Spectrum (functional analysis) Statistical and Nonlinear Physics Nonlinear Sciences - Adaptation and Self-Organizing Systems Modeling and Simulation Bipartite graph Spectral gap Adaptation and Self-Organizing Systems (nlin.AO) Random matrix
Zdroj:	Journal of Physics A
ISSN:	1751-8121 1751-8113
Popis:	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. 17 pages, 6 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd2709c4141643d34a81d8d9e336c089 https://doi.org/10.1088/1751-8121/aa94a9 Zobrazit plný text záznamu