An inequality for functions on the Hamming cube
Combinatorics
2012-07-06 v1
Abstract
We prove an inequality for functions on the discrete cube extending the edge-isoperimetric inequality for sets. This inequality turns out to be equivalent to the following claim about random walks on the cube: Subcubes maximize 'mean first exit time' among all subsets of the cube of the same cardinality.
Cite
@article{arxiv.1207.1233,
title = {An inequality for functions on the Hamming cube},
author = {Alex Samorodnitsky},
journal= {arXiv preprint arXiv:1207.1233},
year = {2012}
}