On the Distribution of the Fourier Spectrum of Halfspaces
Ilias Diakonikolas, Ragesh Jaiswal, Rocco A. Servedio and, Li-Yang Tan, Andrew Wan
TL;DR
This paper sharpens Bourgain's approximation results for noise-stable Boolean functions, specifically halfspaces, providing improved bounds on their Fourier spectrum distribution.
Contribution
It offers an exponential improvement in Bourgain's bounds for halfspaces, under the assumption of noise stability.
Findings
Enhanced bounds on Fourier spectrum distribution for halfspaces
Exponential sharpening of Bourgain's approximation parameters
Improved understanding of noise stability in Boolean functions
Abstract
Bourgain showed that any noise stable Boolean function can be well-approximated by a junta. In this note we give an exponential sharpening of the parameters of Bourgain's result under the additional assumption that is a halfspace.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Mathematical Approximation and Integration · Mathematical Dynamics and Fractals