High-dimensional limit theorems for random vectors in $ell_p^n$-balls
High-dimensional limit theorems for random vectors in $ell_p^n$-balls
复制标题
$ell_p^n$-球中随机向量的高维极限定理
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
C. Thaele
中科院分区：
文献类型：
--
作者：
Z. Kabluchko;J. Prochno;C. Thaele
本文证明了高维$ell_p^n$-球中随机选择的随机向量的q$-模的三种基本极限定理。当随机向量的分布属于Barthe，Guedon，Mendelson和Naor提出的一般类时，我们得到了中心极限定理，中偏差和大偏差原理.它包括归一化体积和锥概率测度以及这些测度的投影作为特例。本文还讨论了$ell_p^n$-球到低维子空间的随机和非随机投影的两个新应用。正文是[Kabluchko，Prochno，塔勒：高维极限定理随机向量在$ell_p^n$-球，Commun.对流（2019）]。
In this article we prove three fundamental types of limit theorems for the $q$-norm of random vectors chosen at random in an $ell_p^n$-ball in high dimensions. We obtain a central limit theorem, a moderate deviations as well as a large deviations principle when the underlying distribution of the random vectors belongs to a general class introduced by Barthe, Guedon, Mendelson, and Naor. It includes the normalized volume and the cone probability measure as well as projections of these measures as special cases. Two new applications to random and non-random projections of $ell_p^n$-balls to lower-dimensional subspaces are discussed as well. The text is a continuation of [Kabluchko, Prochno, Thale: High-dimensional limit theorems for random vectors in $ell_p^n$-balls, Commun. Contemp. Math. (2019)].
随机多胞形：内在体积的中心极限定理
DOI：
10.1090/proc/14000
发表时间：
2018
期刊：
arXiv: Metric Geometry
影响因子：
--
作者：
C. Thale;N. Turchi;F. Wespi
通讯作者：
F. Wespi
影响因子：
1
作者：
Kim, Steven S.;Ramanan, Kavita
通讯作者：
Ramanan, Kavita