Random graphs induced by pairwise markings of Poisson processes    

Günter Last (Karlsruhe Institute of Technology)

Abstract:
We consider a Poisson process on a general phase space.
Independent marking of pairs of the Poisson points gives a random marked graph, supported
by the Poisson points.
In the first part of the lecture we prove some variance inequalities as well as Berry–Esseen type bounds 
for functionals of the random graph.
In the second part of the lecture we apply the general theory to the well-known random connection model on an Euclidean space.

This is joint work with Franz Nestmann (Karlsruhe) and Matthias Schulte (Bern).