正态随机变量
Normal random variables
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中文总结 AI 辅助
本文系统介绍各类正态随机变量，涵盖实、复、瑞利、高维高斯向量及量子版本，并涉及自由概率与随机矩阵。
中文摘要 AI 辅助
这是一篇关于各类正态随机变量的高级导论，其中包含了大部分所需的预备知识。我们首先讨论概率基础、标准中心极限定理以及通常的实正态变量理论，并附有示例、插图和大量公式。接着，我们对复正态变量和瑞利变量进行类似的讨论。然后，我们转向任意维度，讨论高斯向量及其相关的概率分布，并涉及一些泛函分析、几何和物理学内容。最后，我们介绍正态变量的量子版本，特别是来自自由概率和随机矩阵的那些。
英文摘要
This is an advanced introduction to the various types of normal random variables, with most of the needed preliminaries included. We first discuss the probability basics, standard central limits, and the theory of the usual, real normal variables, with examples, illustrations and numerous formulae. Then we go on a similar discussion regarding the complex normal variables, and the Rayleigh variables too. We then move to arbitrary dimensions, with a discussion regarding the Gaussian vectors, and related probability laws, featuring some functional analysis, and geometry and physics too. Finally, we provide an introduction to the quantum versions of the normal variables, and notably to those coming from free probability and random matrices.
发表机构
- University of Cergy-Pontoise（塞吉-蓬图瓦兹大学）
机构由 AI 辅助整理，请以论文原文为准。
