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arXiv · 2311.08163

Some results on fractional vs. expectation thresholds

Thomas Fischer·Yury Person
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Abstract

A conjecture of Talagrand (2010) states that the so-called expectation and fractional expectation thresholds are always within at most some constant factor from each other. Expectation (resp. fractional expectation) threshold $q$ (resp. $q_f$) for an increasing nontrivial class $\mathcal{F}\subseteq 2^X$ allows to locate the threshold for $\mathcal{F}$ within a logarithmic factor (these are important breakthrough results of Park and Pham (2022), resp. Frankston, Kahn, Narayanan and Park (2019)). We will survey what is known about the relation between $q$ and $q_f$ and prove some further special cases of Talagrand's conjecture.

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Thomas Fischer, Yury Person. 2023-11-14. Some results on fractional vs. expectation thresholds. https://arxiv.org/abs/2311.08163

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