Hambly, B. M. and Jordan, J. H. (2003) A random hierarchical lattice: the seriesparallel 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 and respectively. We investigate the effective resistance across the graphs, firstpassage 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 .
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:  29 May 2015 18:16 
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