Percolation in invariant Poisson graphs with i.i.d. degrees
Artikel i vetenskaplig tidskrift, 2012

Let each point of a homogeneous Poisson process in R-d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme which is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components.

prescribed iid degrees

degree sequence

stationary random graphs



Maria Deijfen

Stockholms universitet

Olle Häggström

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

A. E. Holroyd

Microsoft Research

University of British Columbia (UBC)

Arkiv for Matematik

0004-2080 (ISSN)

Vol. 50 41-58