Percolation in invariant Poisson graphs with i.i.d. degrees
Journal article, 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

nearest-neighbor

Author

Maria Deijfen

Stockholm University

Olle Häggström

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

A. E. Holroyd

University of British Columbia (UBC)

Microsoft Research

Arkiv for Matematik

0004-2080 (ISSN)

Vol. 50 1 41-58

Subject Categories

Mathematics

DOI

10.1007/s11512-010-0139-8

More information

Latest update

9/6/2018 1