A stability result for the cube edge isoperimetric inequality

Author: 

Keevash, P
Long, E

Publication Date: 

April 2018

Journal: 

Journal of Combinatorial Theory: Series A

Last Updated: 

2019-04-27T06:15:49.6+01:00

Volume: 

155

DOI: 

10.1016/j.jcta.2017.11.005

page: 

360-375

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 $\varepsilon $-close to a union of $L$ disjoint cubes,
where $L \leq L(K,\varepsilon )$ 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.

Symplectic id: 

688663

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article