Limits of subcritical random graphs and random graphs with excluded minors
Combinatorics
2016-11-28 v2 Probability
Abstract
We prove local convergence results for the uniformly random, labelled or unlabelled, graphs from subcritical families. As an example special case, we prove Benjamini-Schramm convergence for the uniform random unlabelled tree. We introduce a compactification of the space of countable (connected) rooted graphs, and use it to generalise the notion of Benjamini-Schramm convergence in order to allow for vertices of infinite degree in the limit object.
Keywords
Cite
@article{arxiv.1512.03572,
title = {Limits of subcritical random graphs and random graphs with excluded minors},
author = {Agelos Georgakopoulos and Stephan Wagner},
journal= {arXiv preprint arXiv:1512.03572},
year = {2016}
}