Limits of locally–globally convergent graph sequences

By Hamed Hatami, L. Lov'asz, Balázs Szegedy. Geometric and Functional Analysis, 2012

97 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/68d2fcc9b9d5da02ca3cebd7505b0da3469494c7

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In Discrete Mathematics and Combinatorics

1. Á. Backhausz
2. Balázs Szegedy
3. Sourav Chatterjee
4. Svante Janson
5. L. Lov'asz
6. Peter Keevash
7. Oleg Pikhurko
8. Terence Tao

In Geometry and Topology

1. Á. Backhausz
2. Balázs Szegedy
3. Svante Janson
4. L. Lov'asz
5. Sourav Chatterjee
6. Oleg Pikhurko
7. Peter Keevash
8. Tim Austin

In Mathematical Physics

1. Balázs Szegedy

Citations in the corpus

• Action convergence of operators and graphs (2018, background): “, [11, 21]), and corresponding limit objects: graphons, Lp graphons, and graphings.”