arXiv 0811.31832008-11cond-mat.stat-mechmath-phmath.MPmath.PR

Random tree growth by vertex splitting

Francois David, Mark Dukes, Thordur Jonsson, Sigurdur Orn Stefansson

备注：: 47 pages
DOI：: 10.1088/1742-5468/2009/04/P04009

英文摘要：

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 $α$-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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