Some results on fractional vs. expectation thresholds
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2023
- DOI:
- 10.48550/arXiv.2311.08163
- arXiv:
- arXiv:2311.08163
- Bibcode:
- 2023arXiv231108163F
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 17 pages, 0 figures