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arXiv · 1909.05375

Pivotality versus noise stability for monotone transitive functions

Pál Galicza
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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.

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Pál Galicza. 2019-09-11. Pivotality versus noise stability for monotone transitive functions. https://arxiv.org/abs/1909.05375

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