Abstract
We construct a noise stable sequence of transitive, monotone increasing Boolean functions $f_{n}: \{-1,1\}^{k_{n}} \longrightarrow \{-1,1\}$ 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.
Citation
Pál Galicza. "Pivotality versus noise stability for monotone transitive functions." Electron. Commun. Probab. 25 1 - 6, 2020. https://doi.org/10.1214/20-ECP290
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