In this paper, we prove three fundamental types of limit theorems for the [Formula: see text]-norm of random vectors chosen at random in an [Formula: see text]-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, Guédon, 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 [Formula: see text]-balls to lower-dimensional subspaces are discussed as well. The text is a continuation of [Z. Kabluchko, J. Prochno and C. Thäle, High-dimensional limit theorems for random vectors in [Formula: see text]-balls, Commun. Contemp. Math. 21(1) (2019) 1750092].

中文翻译：

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ℓpn 球中随机向量的高维极限定理。二

在本文中，我们证明了 [Formula: see text]-范数在 [Formula: see text] 高维球中随机选择的随机向量范数的三种基本类型的极限定理。当随机向量的基本分布属于 Barthe、Guédon、Mendelson 和 Naor 引入的一般类时，我们得到了中心极限定理、中等偏差以及大偏差原理。它包括归一化体积和圆锥概率测度以及这些测度的投影作为特殊情况。还讨论了将 [公式：参见文本] 球的随机和非随机投影到低维子空间的两个新应用。正文是[Z. Kabluchko、J. Prochno 和 C. Thäle，[公式：见文本]-balls 中随机向量的高维极限定理，Commun。当代。数学。