概率分布的投影：一个测度论的Dvoretzky定理
Projections of probability distributions: A measure-theoretic Dvoretzky theorem
摘要：
许多作者已经研究了高维随机向量的典型高斯边缘的现象;例如，对于$\R^d$上的概率测度，在温和的条件下，如果$d$很大，则大多数一维边缘近似为高斯。在早期的工作中，作者使用熵技术和Stein的方法表明，这种现象持续在有界Lipschitz距离$k$维边缘的$d$维分布，如果$k=o(\sqrt{\log(d)})$。在本文中，一个有点不同的方法是用来表明，这种现象仍然存在，如果$k<\frac{2\log(d)}{\log(\log(d))}$，这种估计是最好的可能。
英文摘要：
Many authors have studied the phenomenon of typically Gaussian marginals of high-dimensional random vectors; e.g., for a probability measure on $\R^d$, under mild conditions, most one-dimensional marginals are approximately Gaussian if $d$ is large. In earlier work, the author used entropy techniques and Stein's method to show that this phenomenon persists in the bounded-Lipschitz distance for $k$-dimensional marginals of $d$-dimensional distributions, if $k=o(\sqrt{\log(d)})$. In this paper, a somewhat different approach is used to show that the phenomenon persists if $k<\frac{2\log(d)}{\log(\log(d))}$, and that this estimate is best possible.
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。
