%0 Journal Article %1 hambly2004random %A Hambly, B. M. %A Jordan, Jonathan %D 2004 %I Applied Probability Trust %J Advances in Applied Probability %K fractal_landscape hierarchical_fractal random_graphs resistance_distance %N 3 %P 824--838 %R 10.1239/aap/1093962236 %T A random hierarchical lattice: the series-parallel graph and its properties %U http://dx.doi.org/10.1239/aap/1093962236 %V 36 %X 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 = 2 1 .

@article{hambly2004random, 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 = 2 1 .}, added-at = {2014-05-05T23:04:07.000+0200}, ajournal = {Adv. in Appl. Probab.}, author = {Hambly, B. M. and Jordan, Jonathan}, biburl = {https://www.bibsonomy.org/bibtex/2865d6158dccf9963c818eb9fc8fe7e6d/peter.ralph}, doi = {10.1239/aap/1093962236}, interhash = {1fafc30e4dc04db45cd66a8641e71727}, intrahash = {865d6158dccf9963c818eb9fc8fe7e6d}, journal = {Advances in Applied Probability}, keywords = {fractal_landscape hierarchical_fractal random_graphs resistance_distance}, month = {09}, number = 3, pages = {824--838}, publisher = {Applied Probability Trust}, timestamp = {2014-05-05T23:04:07.000+0200}, title = {A random hierarchical lattice: the series-parallel graph and its properties}, url = {http://dx.doi.org/10.1239/aap/1093962236}, volume = 36, year = 2004 }