English

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

R2 v1 2026-06-21T21:06:43.655Z