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Fractional vs. Expectation Thresholds: Random Support Case

Authors: Thomas Fischer and Yury Person

Published in: LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)


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. We prove for the unweighted case that this is a.a.s. true when the support is a random hypergraph.

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Thomas Fischer and Yury Person. Fractional vs. Expectation Thresholds: Random Support Case. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 24:1-24:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{fischer_et_al:LIPIcs.AofA.2026.24,
  author =	{Fischer, Thomas and Person, Yury},
  title =	{{Fractional vs. Expectation Thresholds: Random Support Case}},
  booktitle =	{37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)},
  pages =	{24:1--24:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-435-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{381},
  editor =	{Panagiotou, Konstantinos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.24},
  URN =		{urn:nbn:de:0030-drops-262950},
  doi =		{10.4230/LIPIcs.AofA.2026.24},
  annote =	{Keywords: Expectation Threshold, fractional Expectation Threshold, random Hypergraph}
}
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