论文标题
双随机多面体
Doubly random polytopes
论文作者
论文摘要
考虑了生成随机多面体的两步模型。对于参数$ d $，$ m $和$ p $，第一步是生成一个简单的polytope $ p $，其面积由$ m $统一的随机超平面在$ \ mathbb {r}^d $中切成单位球，第二步是第二步，第二步是独立于$ p $ $ p $ $ p $的$ p $ p $ p $ p $ p $ q p $ q。我们建立了$ Q $ a $ m $和$ p $的$ q $近似于单位球的结果，以及在合并式复杂性上$ q $的渐近性，对于$ p $的某些制度。
A two-step model for generating random polytopes is considered. For parameters $d$, $m$, and $p$, the first step is to generate a simple polytope $P$ whose facets are given by $m$ uniform random hyperplanes tangent to the unit sphere in $\mathbb{R}^d$, and the second step is to sample each vertex of $P$ independently with probability $p$ and let $Q$ be the convex hull of the sampled vertices. We establish results on how well $Q$ approximates the unit sphere in terms of $m$ and $p$ as well as asymptotics on the combinatorial complexity of $Q$ for certain regimes of $p$.
