DOI: 10.1140/epjc/s2002-01102-6
Vertex counting: Statistical distribution of vertices in large sets of tree diagrams
P. Draggiotis and R. KleissUniversity of Nijmegen, Nijmegen, The Netherlands
(Received: 12 September 2002 / Published online: 24 January 2003 )
Abstract
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
that the distribution's "fine structure", arising from
topological sum rules, can be obtained.
© Società Italiana di Fisica, Springer-Verlag 2003
