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 and
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
.
| 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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