Full Connectivity: Corners, Edges and Faces

  title={Full Connectivity: Corners, Edges and Faces},
  author={Justin P. Coon and Carl P. Dettmann and Orestis Georgiou},
  journal={Journal of Statistical Physics},
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… 
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