对称随机向量的中心极限问题
The central limit problem for random vectors with symmetries
摘要：
受凸体中心极限问题的启发，我们研究了高维随机向量的线性泛函在各种对称下的正规逼近。特别是，我们得到的结果是coordinatewise对称的分布，均匀的正规单纯形，或球对称。我们的证明是基于斯坦因的方法交换对，据我们所知，这种方法以前没有被用于凸几何，我们给一个简单的介绍经典的方法。球对称的情况下处理的变化斯坦的方法，这是适应连续对称。
英文摘要：
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.
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