Journal article

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

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. 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 finda phase transition at p = 1/2. © Applied Probability Trust 2004.

Publication status:: Published

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APA Style

Hambly, B., & Jordan, J. (2004). A random hierarchical lattice: The series-parallel graph and its properties. ADVANCES IN APPLIED PROBABILITY, 36(3), 824–838.

MLA Style

Hambly, B., and J. Jordan. “A Random Hierarchical Lattice: The Series-Parallel Graph and Its Properties.” ADVANCES IN APPLIED PROBABILITY, vol. 36, no. 3, 2004, pp. 824–38.

Chicago Style

Hambly, B, and J Jordan. 2004. “A Random Hierarchical Lattice: The Series-Parallel Graph and Its Properties.” ADVANCES IN APPLIED PROBABILITY 36 (3): 824–38.
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Publisher copy:: 10.1239/aap/1093962236

Authors

+ Hambly, B More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Jordan, J More by this author

Role:: Author

Journal:: ADVANCES IN APPLIED PROBABILITY More from this journal
Volume:: 36
Issue:: 3
Pages:: 824-838
Publication date:: 2004-09-01
DOI:: 10.1239/aap/1093962236
ISSN:: 0001-8678

Keywords:: effective resistance

hierarchical lattice

first-passage percolation

phase transition

Cheeger constants
Pubs id:: pubs:10397
UUID:: uuid:fd21bacf-d2a5-4ff1-b130-e303bf008494
Local pid:: pubs:10397
Source identifiers:: 10397
Deposit date:: 2012-12-19

Terms of use

Copyright date:: 2004

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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