与高斯凸包相关的反例
A counter-example linked to Gaussian convex hulls
AI总结：
研究独立中心高斯随机元素及其闭凸包的弱收敛性，展示当初始序列弱收敛时，归一化凸包收敛到极限分布的集中椭球，但若放松弱收敛假设，极限集可为任意凸紧集。
摘要：
我们考虑分离Banach空间中独立中心高斯随机元素及其连续闭凸包序列。如果初始元素弱收敛到某个极限，则如Davydov-Paulauskas(2024)所示，其归一化凸包以概率1收敛到极限分布的集中椭球。本文的目标是展示当放松初始序列的弱收敛假设时，极限集可以是任意凸紧集。
英文摘要：
We consider the sequence of independent centered Gaussian random elements of a separable Banach space and their consecutive closed convex hulls. If inicial elements converge weakly to some limite, then, as shown in Davydov- Paulauskas (2024), its normalized convex hulls converge, with probability 1, to the concentration ellipsoid of the limiting distribution. The goal of the present note is to show that if the assumption of weak convergence of the initial sequence is relaxed, than the limit set can be an arbitrary convex compact set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
