A new approach to prove weak convergence of random polytopes on the space of compact convex sets is presented. This is used to show that the profile of the rescaled Schläfli random cone of a random conical tessellation, generated by n independent and uniformly distributed random linear hyperplanes in $\mathbb {R}^{d+1}$ , weakly converges to the typical cell of a stationary and isotropic Poisson hyperplane tessellation in $\mathbb {R}^d$ , as $n\to \infty $ .

中文翻译：

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一种随机锥和多胞体弱收敛的新方法

提出了一种证明紧凸集空间上随机多胞体弱收敛的新方法。这用于表明随机锥形细分的重新缩放 Schläfli 随机锥的轮廓，由 $\mathbb {R}^{d+1}$ 中 的n 个独立且均匀分布的随机线性超平面 生成，弱收敛到典型的 $\mathbb {R}^d$ 中的固定和各向同性泊松超平面细分的单元格 ，作为 $n\to \infty $ 。