An Inequality for Functions on the Hamming Cube

作者:Samorodnitsky Alex*
来源:Combinatorics Probability & Computing, 2017, 26(3): 468-480.
DOI:10.1017/S0963548316000432

摘要

We prove an inequality for functions on the discrete cube {0,1}(n) 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.

  • 出版日期2017-5