English

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.

Keywords

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