Gaussian Bounds for Noise Correlation of Functions
Probability
2009-06-01 v6 Combinatorics
Statistics Theory
Statistics Theory
Abstract
In this paper we derive tight bounds on the expected value of products of {\em low influence} functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated probability spaces, on a generalization of an invariance principle recently obtained with O'Donnell and Oleszkiewicz for multilinear polynomials with low influences and bounded degree and on properties of multi-dimensional Gaussian distributions. The results derived here have a number of applications to the theory of social choice in economics, to hardness of approximation in computer science and to additive combinatorics problems.
Cite
@article{arxiv.math/0703683,
title = {Gaussian Bounds for Noise Correlation of Functions},
author = {Elchanan Mossel},
journal= {arXiv preprint arXiv:math/0703683},
year = {2009}
}
Comments
Typos and references corrected