Full Connectivity: Corners,Edges and Faces |
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Authors: | Justin Coon Carl P Dettmann Orestis Georgiou |
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Institution: | 1.Toshiba Telecommunications Research Laboratory,Bristol,UK;2.School of Mathematics,University of Bristol,Bristol,UK;3.Max-Planck-Institute for the Physics of Complex Systems,Dresden,Germany |
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Abstract: | We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different models. |
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