论文标题
高维的椭圆形分布的随机简短量
The volume of random simplices from elliptical distributions in high dimension
论文作者
论文摘要
考虑到$ \ mathbb {r}^n $带有$ p \ leq n $的尺寸$ p $的随机简单和更一般的随机凸体，这是由具有椭圆形分布的随机向量生成的。在高维度中，也就是说，如果$ p \ to \ infty $和$ n \ to \ to \ infty $以$ p/n \toγ\ in（0,1）$（0,1）$，则显示了中央和稳定的限制定理，用于随机简单和随机凸形体的对数体积。结果来自相关的中央限制定理，用于$ p \ times n $随机矩阵的log-diterminant，其行是具有椭圆形分布的随机矢量的副本，也是建立的。
Random simplices and more general random convex bodies of dimension $p$ in $\mathbb{R}^n$ with $p\leq n$ are considered, which are generated by random vectors having an elliptical distribution. In the high-dimensional regime, that is, if $p\to\infty$ and $n\to\infty$ in such a way that $p/n\toγ\in(0,1)$, a central and a stable limit theorem for the logarithmic volume of random simplices and random convex bodies is shown. The result follows from a related central limit theorem for the log-determinant of $p\times n$ random matrices whose rows are copies of a random vector with an elliptical distribution, which is established as well.
