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. The expectation threshold $q$ for an increasing class $\mathcal{F}\subseteq 2^X$ allows to locate the threshold for $\mathcal{F}$ within a logarithmic factor. The same holds for the fractional expectation threshold $q_f$. 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.
@article{10_37236_12611,
author = {Thomas Fischer and Yury Person},
title = {Some results on fractional vs. expectation thresholds},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/12611},
zbl = {8097667},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12611/}
}
TY - JOUR
AU - Thomas Fischer
AU - Yury Person
TI - Some results on fractional vs. expectation thresholds
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/12611/
DO - 10.37236/12611
ID - 10_37236_12611
ER -
%0 Journal Article
%A Thomas Fischer
%A Yury Person
%T Some results on fractional vs. expectation thresholds
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/12611/
%R 10.37236/12611
%F 10_37236_12611
Thomas Fischer; Yury Person. Some results on fractional vs. expectation thresholds. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/12611
