Full Connectivity: Corners, edges and faces

Details Full Connectivity: Corners, edges and faces Full Connectivity: Corners, edges and faces

2012-01-15

arxiv.org/abs/1201.3123v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

28 pages, 8 figures

Scientific paper

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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