An exactly solvable special case of the vertex splitting model
by
Sigurdur Stefansson(Nordita)
→
Europe/Stockholm
Description
I will introduce a recent model of randomly growing trees, referred to as the vertex splitting model [1]. In each time step a vertex is selected at random and split into two vertices which are joined by a new edge. This model originates from a related model of growing trees which is equivalent to a model of random RNA folding. I will explain this origin briefly and then discuss some mathematical properties of the model. Some exact results have been obtained on the vertex degree distribution but other results on e.g. the tree profile (Hausdorff dimension) are in general not mathematically rigorous and depend on scaling assumptions. I will conclude by presenting a recently discovered, non-trivial special case of the model where one can do calculations without using these scaling assumptions.
[1] François David, Mark Dukes, Thordur Jonsson, Sigurður Örn Stefánsson. Random tree growth by vertex splitting. Journal of Statistical Mechanics (2009), no. 4, P04009. arxiv: 0811.3183
