Statistics Papers

Document Type

Journal Article

Date of this Version

6-2012

Publication Source

Israel Journal of Mathematics

Volume

189

Issue

1

Start Page

347

Last Page

396

DOI

10.1007/s11856-011-0181-7

Abstract

Gaussian noise stability results have recently played an important role in proving results in hardness of approximation in computer science and in the study of voting schemes in social choice. We prove a new Gaussian noise stability result generalizing an isoperimetric result by Borell on the heat kernel and derive as applications:

  • An optimality result for majority in the context of Condorcet voting.

  • A proof of a conjecture on “cosmic coin tossing” for low influence functions.

We also discuss a Gaussian noise stability conjecture which may be viewed as a generalization of the “Double Bubble” theorem and show that it implies:

  • A proof of the “Plurality is Stablest Conjecture”.

  • That the Frieze-Jerrum SDP for MAX-q-CUT achieves the optimal approximation factor assuming the Unique Games Conjecture.

Copyright/Permission Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/s11856-011-0181-7.

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Date Posted: 27 November 2017

This document has been peer reviewed.