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Almost sure convergence of vertex degree densities in the vertex splitting model

Almost sure convergence of vertex degree densities in the vertex splitting model

We study the limiting degree distribution of the vertex splitting model introduced in Ref.[3 David, F.; Dukes, M.; Jonsson, T.; Stefansson, S.Ö. Random tree growth by vertex splitting. J. Statist. Mech. Theory Exp. 2009, 04. doi:10.1088/1742-5468/2009/04/P04009. [Google Scholar]]. This is a model of randomly growing ordered trees, where in each …