发表机构
New York University（纽约大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究布尔格上的 $p$-扩散测度，证明大集合族下无 $p$-扩散测度支撑于未覆盖集族，解决 Talagrand 离散凸性问题的分数版本，并建立两个比较定理。
AI 中文摘要
我们研究布尔格上的 $p$-扩散概率测度。我们证明，如果一个集合族在乘积 Bernoulli-$p$ 测度下足够大，那么不存在 $p$-扩散测度能支撑在该族中未被其两个成员并集覆盖的集合族上，从而回答了 Talagrand 离散凸性问题的分数版本。由此，我们建立了 $p$-扩散测度与乘积 Bernoulli-$p$ 测度之间的两个比较定理。
英文摘要
We study $p$-spread probability measures on the Boolean lattice. We show that if a family of sets $A$ is large under the product Bernoulli-$p$ measure, then no $p$-spread measure can be supported on sets that are not covered by the union of two members of $A$, answering the fractional version of Talagrand's discrete convexity problem. Consequently, we establish a coupling theorem between $p$-spread and product Bernoulli-$p$ measures.
CommentsIncorporated recent developments in an expanded introduction
