Gaussian Bounds for Noise Correlation of Functions

Details Gaussian Bounds for Noise Correlation of Functions Gaussian Bounds for Noise Correlation of Functions

2007-03-22

arxiv.org/abs/math/0703683v6

Mathematics

Probability

Typos and references corrected

Scientific paper

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.

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