eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-08-01
10:1
10:11
10.4230/LIPIcs.CCC.2017.10
article
Noise Stability Is Computable and Approximately Low-Dimensional
De, Anindya
Mossel, Elchanan
Neeman, Joe
Questions of noise stability play an important role in hardness of approximation in computer science as well as in the theory of voting. In many applications, the goal is to find an optimizer of noise stability among all possible partitions of R^n for n >= 1 to k parts with given Gaussian measures mu_1, ..., mu_k. We call a partition epsilon-optimal, if its noise stability is optimal up to an additive epsilon. In this paper, we give an explicit, computable function n(epsilon) such that an epsilon-optimal partition exists in R^{n(epsilon)}. This result has implications for the computability of certain problems in non-interactive simulation, which are addressed in a subsequent work.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol079-ccc2017/LIPIcs.CCC.2017.10/LIPIcs.CCC.2017.10.pdf
Gaussian noise stability; Plurality is stablest; Ornstein Uhlenbeck operator