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 |
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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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