PreprintCC0arXiv
Small Influential Coalitions in [0,1]n via the Junta Theorem
Abstract
Every monotone Boolean function on the continuous cube admits a coalition of O(n/(εlog n)) coordinates that can force a fixed output (either zero or one) with probability at least 1−ε. This old conjecture of mine was recently proven by Chattopadhyay and Gurumukhani~\cite{CG}. This writeup contains a simplification of their proof, generated by AI after suggesting the use of the junta theorem of~\cite{F98} and the discretization procedure of ~\cite{F04}.
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BibTeX
@misc{friedgut2026small,
title = {{Small Influential Coalitions in $[0,1]^n$ via the Junta Theorem}},
author = {Ehud Friedgut},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03086},
eprint = {2610.03086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03086},
note = {CC0},
}
RIS
TY - UNPB
TI - Small Influential Coalitions in [0,1]^n via the Junta Theorem
AU - Ehud Friedgut
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03086
UR - https://arxiv.org/abs/2610.03086
AB - Every monotone Boolean function on the continuous cube admits a coalition of O(n/(εlog n)) coordinates that can force a fixed output (either zero or one) with probability at least 1−ε. This old conjecture of mine was recently proven by Chattopadhyay and Gurumukhani~\cite{CG}. This writeup contains a simplification of their proof, generated by AI after suggesting the use of the junta theorem of~\cite{F98} and the discretization procedure of ~\cite{F04}.
ER -