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Analytical solution of the voter model on uncorrelated networks

AutorVázquez, Federico ; Eguíluz, Víctor M.
Palabras claveStatistical mechanics
Fecha de publicación9-jun-2008
EditorDeutsche Physikalische Gesellschaft
Institute of Physics Publishing
CitaciónNew Journal of Physics 10: 063011 (2008)
ResumenWe present a mathematical description of the voter model dynamics on heterogeneous networks. When the average degree of the graph is μ ≤ 2 the system reaches complete order exponentially fast. For μ > 2, a finite system falls, before it fully orders, in a quasistationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to [(μ-2)/3(μ-1)], while an infinite large system stays ad infinitum in a partially ordered stationary active state. The mean life time of the quasistationary state is proportional to the mean time to reach the fully ordered state T, which scales as T ~ [(μ-1)μ^2 N/(μ-2)μ_2], where N is the number of nodes of the network, and μ_2 is the second moment of the degree distribution. We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.
Descripción19 pages, 8 figures.-- ArXiv pre-print available at: http://arxiv.org/abs/0803.1686
Versión del editorhttp://dx.doi.org/10.1088/1367-2630/10/6/063011
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