Limits of locally-globally convergent graph sequences

Hatami, H. and Lovász, László and Szegedy, Balázs (2014) Limits of locally-globally convergent graph sequences. GEOMETRIC AND FUNCTIONAL ANALYSIS, 24 (1). pp. 269-296. ISSN 1016-443X

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Abstract

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

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