Random tree growth by vertex splitting

Details Random tree growth by vertex splitting Random tree growth by vertex splitting

2008-11-19

arxiv.org/abs/0811.3183v3

Physics

Condensed Matter

Statistical Mechanics

47 pages

Scientific paper

10.1088/1742-5468/2009/04/P04009

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalises the preferential attachment model and Ford's $\alpha$-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from one to infinity, depending on the parameters of the model.

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