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Note on a conjecture of Talagrand: expectation thresholds vs. fractional expectation thresholds

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arxiv 2412.00917 v1 pith:36HNETUT submitted 2024-12-01 math.CO math.PR

Quentin Dubroff , Jeff Kahn , Jinyoung Park This is my paper · ORCID
classification math.COmath.PR
keywords conjectureexpectationthresholdstalagrandfractionalselectorversionbednorz
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We show that a restricted version of a conjecture of M. Talagrand on the relation between "expectation thresholds" and "fractional expectation thresholds" follows easily from a strong version of a second conjecture of Talagrand, on "selector processes." The selector process conjecture was proved by Park and Pham, and the quantitative strengthening used here is due to Bednorz, Martynek, and Meller.

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  1. Further remarks on fractional vs. expectation thresholds

    math.CO 2025-05 conditional novelty 6.0 of 10

    The authors verify Talagrand's threshold conjecture for the family of ℓ-uniform hypergraph cliques, with a uniform constant L = 2^12 e^16 for large ground sets.

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