A simple reduction from a biased measure on the discrete cube to the uniform measure

Authors:
Nathan Keller
Affiliations:
-
Venue:
European Journal of Combinatorics
Year:
2012

Citing 4
Cited 0

Influences in Product Spaces: KKL and BKKKL Revisited

Combinatorics, Probability and Computing
The influence of variables on Boolean functions

SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Decision trees and influences of variables over product probability spaces

Combinatorics, Probability and Computing
On the influences of variables on boolean functions in product spaces

Combinatorics, Probability and Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that certain statements related to the Fourier-Walsh expansion of functions with respect to a biased measure on the discrete cube can be deduced from the respective results for the uniform measure by a simple reduction. In particular, we present simple generalizations to the biased measure @m"p of the Bonami-Beckner hypercontractive inequality, and of Talagrand's lower bound on the size of the boundary of subsets of the discrete cube. Our generalizations are tight up to constant factors.