A stability result for the cube edge isoperimetric inequality

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  • University of Oxford


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