A stability result for the cube edge isoperimetric inequality

作者：Keevash Peter^*; Long Eoin

来源：Journal of Combinatorial Theory - Series A, 2018, 155: 360-375.

DOI：10.1016/j.jcta.2017.11.005

• Isoperimetric inequality
• Hypercube
• Boolean analysis
• Stability

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 epsilon-close to a union of L disjoint cubes, where L <= L(K, epsilon) 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.

• 出版日期2018-4