Thresholds versus fractional expectation-thresholds

Proving a conjecture of Talagrand, a fractional version of the “expectation-threshold” conjecture of Kalai and the second author, we show that p c (F) = O(q f (F) log l(F)) for any increasing family F on a finite set X, where p c (F) and qf(F) are the threshold and “fractional expectation-threshold”...

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Bibliographic Details
Published in:Annals of mathematics 2021-09, Vol.194 (2), p.475-495
Main Authors: Frankston, Keith, Kahn, Jeff, Narayanan, Bhargav, Park, Jinyoung
Format: Article
Language:English
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