Limits of locally-globally convergent graph sequences

作者:Hatami Hamed*; Lovasz Laszlo; Szegedy Balazs
来源:Geometric and Functional Analysis, 2014, 24(1): 269-296.
DOI:10.1007/s00039-014-0258-7

摘要

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.

  • 出版日期2014-2
  • 单位McGill