The Mathematical Institute, University of Oxford, Eprints Archive

A random hierarchical lattice: the series-parallel graph and its properties

Hambly, B. M. and Jordan, J. H. (2003) A random hierarchical lattice: the series-parallel graph and its properties. Advances in Applied Probability . (In Press)

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Abstract

We consider a sequence of random graphs constructed by a hierarchical procedure. The construction replaces existing edges by pairs of edges in series or parallel with probability $p$ and $1-p$ respectively. We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. In each case we find a phase transition at $p=1/2$.

Item Type:Article
Subjects:O - Z > Probability theory and stochastic processes
Research Groups:Stochastic Analysis Group
Oxford Centre for Industrial and Applied Mathematics
ID Code:112
Deposited By:Ben Hambly
Deposited On:04 Aug 2004
Last Modified:20 Jul 2009 14:18

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