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A stability result for the cube edge isoperimetric inequality

Abstract:
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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1016/j.jcta.2017.11.005

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
Elsevier Publisher's website
Journal:
Journal of Combinatorial Theory, Series A Journal website
Volume:
155
Pages:
360-375
Publication date:
2017-11-24
Acceptance date:
2017-08-23
DOI:
ISSN:
0097-3165
Pubs id:
pubs:688663
URN:
uri:621130cf-eed4-456d-b640-0dcd4fabf5cd
UUID:
uuid:621130cf-eed4-456d-b640-0dcd4fabf5cd
Local pid:
pubs:688663

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