English

Pivotality versus noise stability for monotone transitive functions

Probability 2019-09-13 v1

Abstract

We construct a noise stable sequence of transitive, monotone increasing Boolean functions fn:{1,1}kn{1,1}f_n: \{-1,1\}^{k_n} \longrightarrow \{-1,1\} which admit many pivotals with high probability. We show that such a sequence is volatile as well, and thus it is also an example of a volatile and noise stable sequence of transitive, monotone functions.

Keywords

Cite

@article{arxiv.1909.05375,
  title  = {Pivotality versus noise stability for monotone transitive functions},
  author = {Pál Galicza},
  journal= {arXiv preprint arXiv:1909.05375},
  year   = {2019}
}
R2 v1 2026-06-23T11:12:54.537Z