论文标题
Kahn-Kalai猜想的证明
A Proof of the Kahn-Kalai Conjecture
论文作者
论文摘要
在有限的集合$ x $，$ x $，$ x $，$ x $，$ mathcal {f}）上证明了卡恩和卡莱的``期望 - 阈值''的猜想，我们表明，对于任何增加的属性$ \ mathcal {f} $ $ p_c（\ Mathcal {f}）$和$ q（\ Mathcal {f}）$是$ \ Mathcal {f} $的阈值和``期望阈值'''，而$ \ ell（\ nathcal {f}）$是最大$ 2 $ $ 2 $和MINAL $ a的最高成员。
Proving the ``expectation-threshold'' conjecture of Kahn and Kalai, we show that for any increasing property $\mathcal{F}$ on a finite set $X$, $$p_c(\mathcal{F})=O(q(\mathcal{F})\log \ell(\mathcal{F})),$$ where $p_c(\mathcal{F})$ and $q(\mathcal{F})$ are the threshold and ``expectation threshold'' of $\mathcal{F}$, and $\ell(\mathcal{F})$ is the maximum of $2$ and the maximum size of a minimal member of $\mathcal{F}$.
