Limits of local-global convergent graph sequences

The colored neighborhood metric for sparse graphs was introduced by Bollobás 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...

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Bibliographic Details
Published in:arXiv.org 2013-08
Main Authors: Hatami, Hamed, Lovász, László, Szegedy, Balázs
Format: Article
Language:English
Subjects:
Convergence
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Summary:The colored neighborhood metric for sparse graphs was introduced by Bollobás 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.
ISSN:2331-8422