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Creators/Authors contains: "Park, Jinyoung"

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  1. Free, publicly-accessible full text available March 14, 2026
  2. Free, publicly-accessible full text available February 1, 2026
  3. Abstract We address a special case of a conjecture of M. Talagrand relating two notions of “threshold” for an increasing family of subsets of a finite setV. The full conjecture implies equivalence of the “Fractional Expectation‐Threshold Conjecture,” due to Talagrand and recently proved by the authors and B. Narayanan, and the (stronger) “Expectation‐Threshold Conjecture” of the second author and G. Kalai. The conjecture under discussion here says there is a fixedLsuch that if, for a given , admits withand(a.k.a.  isweakly p‐small), then admits such a taking values in ( is‐small). Talagrand showed this when is supported on singletons and suggested, as a more challenging test case, proving it when is supported on pairs. The present work provides such a proof. 
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