论文标题
投影几何形状中的随机铭文多型
Random inscribed polytopes in projective geometries
论文作者
论文摘要
我们建立了中心限制定理，用于在射击或芬斯勒的几何形状中自然铭刻的多面体的自然体积。另外，获得双重体积的正常近似值和随机多面体集的平均宽度。我们通过证明从光滑凸体边界的随机点的加权体积的加权体积根据欧几里得空间中的正且连续的密度选择的随机点的加权体积来推断这些结果。在背景中，是对独立随机变量功能的加权表面体和浆果 - 埃森界限的几何估计。
We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation of dual volumes and the mean width of random polyhedral sets are obtained. We deduce these results by proving a general central limit theorem for the weighted volume of the convex hull of random points chosen from the boundary of a smooth convex body according to a positive and continuous density in Euclidean space. In the background are geometric estimates for weighted surface bodies and Berry-Esseen bounds for functionals of independent random variables.
