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An Inequality for Functions on the Hamming Cube

Part of: Combinatorial probability Extremal combinatorics

Published online by Cambridge University Press:  29 March 2017

ALEX SAMORODNITSKY
ALEX SAMORODNITSKY*
Affiliation:
School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail: [email protected])
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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.

MSC classification

Primary: 05D05: Extremal set theory
Secondary: 60C05: Combinatorial probability
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 3 , May 2017 , pp. 468 - 480
Copyright
Copyright © Cambridge University Press 2017 

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