Bipartite Stable Poisson Graphs on R
2012 (English)In: Markov processes and related fields, ISSN 1024-2953, Vol. 18, no 4, 583-594 p.Article in journal (Refereed) Published
Let red and blue points be distributed on R according to two independent Poisson processes R and B and let each red (blue) point independently be equipped with a random number of half-edges according to a probability distribution nu (mu). We consider translation-invariant bipartite random graphs with vertex classes defined by the point sets of R, and B, respectively, generated by a scheme based on the Gale - Shapley stable marriage for perfectly matching the half-edges. Our main result is that, when all vertices have degree 2, then the resulting graph almost surely does not contain an infinite component. The two-color model is hence qualitatively different from the one-color model, where Deijfen, Holroyd and Peres have given strong evidence that there is an infinite component. We also present simulation results for other degree distributions.
Place, publisher, year, edition, pages
2012. Vol. 18, no 4, 583-594 p.
Poisson process, random graph, degree distribution, percolation, matching
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:su:diva-87670ISI: 000313221100001OAI: oai:DiVA.org:su-87670DiVA: diva2:606082