A stability result for the cube edge isoperimetric inequality

Peter Keevash, Eoin Long

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
101 Downloads (Pure)


We prove the following stability version of the edge isoperimetric inequality for the cube: any subset of the cube with average boundary degree within K of the minimum possible is ε-close to a union of L disjoint cubes, where L≤ L(K, ε) is independent of the dimension. This extends a stability result of Ellis, and can viewed as a dimension-free version of Friedgut's junta theorem.
Original languageEnglish
Pages (from-to)360-375
Number of pages16
JournalJournal of Combinatorial Theory, Series A
Early online date24 Nov 2017
Publication statusPublished - 1 Apr 2018


  • Isoperimetric inequality.
  • hypercube
  • Boolean analysis
  • Stability


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