Corpus ID: 204943191

# Thresholds versus fractional expectation-thresholds

@article{Frankston2019ThresholdsVF,
title={Thresholds versus fractional expectation-thresholds},
author={Keith Frankston and J. Kahn and Bhargav P. Narayanan and Jinyoung Park},
journal={ArXiv},
year={2019},
volume={abs/1910.13433}
}
Proving a conjecture of Talagrand, a fractional version of the 'expectation-threshold' conjecture of Kalai and the second author, we show for any increasing family $F$ on a finite set $X$ that $p_c (F) =O( q_f (F) \log \ell(F))$, where $p_c(F)$ and $q_f(F)$ are the threshold and 'fractional expectation-threshold' of $F$, and $\ell(F)$ is the largest size of a minimal member of $F$. This easily implies several heretofore difficult results and conjectures in probabilistic combinatorics, including… Expand

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