论文标题
最佳收敛速率的公园定理
The Park-Pham Theorem with Optimal Convergence Rate
论文作者
论文摘要
Park和Pham最近证明了Kahn-Kalai猜想是图形和超图阈值领域的重大突破。他们的结果使概率结构具有$ 1-ε$的机会有机会实现给定的单调属性的阈值。尽管它们在其他参数中的限制是最佳选择的任何固定$ε$的常数因素，但它没有对$ε$的最佳依赖性为$ε\ rightarrow 0 $。在这篇简短的论文中，我们证明了具有最佳$ε$依赖性的Park-Pham定理版本。
Park and Pham's recent proof of the Kahn-Kalai conjecture was a major breakthrough in the field of graph and hypergraph thresholds. Their result gives an upper bound on the threshold at which a probabilistic construction has a $1-ε$ chance of achieving a given monotone property. While their bound in other parameters is optimal up to constant factors for any fixed $ε$, it does not have the optimal dependence on $ε$ as $ε\rightarrow 0$. In this short paper, we prove a version of the Park-Pham Theorem with optimal $ε$-dependence.
