FKN Theorem on the biased cube
Combinatorics
2013-11-14 v1
Abstract
In this note we consider Boolean functions defined on the discrete cube equipped with a biased product probability measure. We prove that if the spectrum of such a function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Moreover, in the symmetric case we prove that if a [-1,1]-valued function defined on the discrete cube is close to a certain affine function, then it is also close to a [-1,1]-valued affine function.
Cite
@article{arxiv.1311.3179,
title = {FKN Theorem on the biased cube},
author = {Piotr Nayar},
journal= {arXiv preprint arXiv:1311.3179},
year = {2013}
}
Comments
10 pages