Finite graphs and amenability

Details Finite graphs and amenability Finite graphs and amenability

2012-04-02

arxiv.org/abs/1204.0449v1

Mathematics

Functional Analysis

Scientific paper

Hyperfiniteness or amenability of measurable equivalence relations and group actions has been studied for almost fifty years. Recently, unexpected applications of hyperfiniteness were found in computer science in the context of testability of graph properties. In this paper we propose a unified approach to hyperfiniteness. We establish some new results and give new proofs of theorems of Schramm, Lov\'asz, Newman-Sohler and Ornstein-Weiss.

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