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
Dirac-type theorems in random hypergraphs
Sharp threshold rates for random codes
Hitting times for Shamir's Problem
Set system intersections can typically be blown up
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Improved bounds for the sunflower lemma
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  • D. Karger
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  • STOC
  • 2020
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