非均匀卡恩-卡莱猜想的简单证明

Pub Date : 2024-07-04 DOI:10.1137/23m1587075

Bryan Park, Jan Vondrák

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引用次数: 0

摘要

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2089-2094 页，2024 年 9 月。摘要。我们重温了最近由 Park 和 Pham 以惊人的方式证明的 Kahn-Kalai 猜想，并提出了一个略微重新表述的简单证明，它有几个优点：(1) 它适用于非均匀积度量；(2) 即使在抽样概率接近 1 的情况下，它也给出了接近最优的约束；(3) 它为每一个[math]有界集合系统给出了一个干净的[math]约束[math]。

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A Simple Proof of the Nonuniform Kahn–Kalai Conjecture

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2089-2094, September 2024.
Abstract. We revisit the Kahn–Kalai conjecture, recently proved in striking fashion by Park and Pham, and present a slightly reformulated simple proof which has a few advantages: (1) it works for nonuniform product measures, (2) it gives near-optimal bounds even for sampling probabilities close to 1, (3) it gives a clean bound of [math] for every [math]-bounded set system, [math].

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