Pivotality versus noise stability for monotone transitive functions

Abstract

We construct a noise stable sequence of transitive, monotone increasing Boolean functions $f_n:\{-1,1{\}}^{k_n}⟶\{-1,1\}$ 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.