An Inequality for Functions on the Hamming Cube

Alex Samorodnitsky

doi:10.1017/S0963548316000432

An Inequality for Functions on the Hamming Cube

Alex Samorodnitsky

The Rachel and Selim Benin School of Engineering and Computer Science

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	468-480
Number of pages	13
Journal	Combinatorics Probability and Computing
Volume	26
Issue number	3
DOIs	https://doi.org/10.1017/S0963548316000432
State	Published - 1 May 2017

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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abstract = "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.",

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An Inequality for Functions on the Hamming Cube

Abstract

All Science Journal Classification (ASJC) codes

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