Limits of locally-globally convergent graph sequences

Hamed Hatami, László Lovász, Balázs Szegedy

Research output: Contribution to journalArticle

30 Citations (Scopus)


The colored neighborhood metric for sparse graphs was introduced by Bollobás and Riordan [BR11]. The corresponding convergence notion refines a convergence notion introduced by Benjamini and Schramm [BS01]. 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.

Original languageEnglish
Pages (from-to)269-296
Number of pages28
JournalGeometric and Functional Analysis
Issue number1
Publication statusPublished - Feb 2014

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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