Vertex Counting: Statistical Distribution of Vertices in Large Sets of   Tree Diagrams
  We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and we compute the mean and variance of this distribution for several theories. We show the distribution's `fine structure', arising from topological sum rules, can be obtained. 
Petros Draggiotis, Ronald Kleiss