Limits of local-global convergent graph sequences
Combinatorics
2013-08-23 v2 Dynamical Systems
Probability
Abstract
The colored neighborhood metric for sparse graphs was introduced by Bollob\'as and Riordan. The corresponding convergence notion refines a convergence notion introduced by Benjamini and Schramm. We prove that even in this refined sense, the limit of a convergent graph sequence (with uniformly bounded degree) can be represented by a graphing. We study various topics related to this convergence notion such as: Bernoulli graphings, factor of i.i.d. processes and hyperfiniteness.
Keywords
Cite
@article{arxiv.1205.4356,
title = {Limits of local-global convergent graph sequences},
author = {Hamed Hatami and László Lovász and Balázs Szegedy},
journal= {arXiv preprint arXiv:1205.4356},
year = {2013}
}
Comments
25 pages