Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Finite graphs and amenability
AU - Elek, Gábor
PY - 2012/11/1
Y1 - 2012/11/1
N2 - 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, Lovász, Newman–Sohler and Ornstein–Weiss.
AB - 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, Lovász, Newman–Sohler and Ornstein–Weiss.
KW - Amenability
KW - Hyperfiniteness
KW - Graphs
KW - Graphings
U2 - 10.1016/j.jfa.2012.08.021
DO - 10.1016/j.jfa.2012.08.021
M3 - Journal article
VL - 263
SP - 2593
EP - 2614
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 9
ER -