高维空间奇度

IF 1.8 4区数学 Q1 STATISTICS & PROBABILITY

American Statistician Pub Date : 2025-05-15 DOI:10.1080/00031305.2025.2505507

Haim Bar, Vladimir Pozdnyakov

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引用次数: 0

摘要

Talagrand在1996年的论文中强调，独立随机变量的大数定律（LLN）可以看作是多维积空间的一个几何性质。这种现象被称为度量的集中。为了说明几何和概率论之间的这种深刻联系，我们考虑了多维欧几里德空间中一个看似棘手的几何问题，并使用标准概率工具（如LLN和中心极限定理（CLT））来解决它。

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High Dimensional Space Oddity

In his 1996 paper, Talagrand highlighted that the Law of Large Numbers (LLN) for independent random variables can be viewed as a geometric property of multidimensional product spaces. This phenomenon is known as the concentration of measure. To illustrate this profound connection between geometry and probability theory, we consider a seemingly intractable geometric problem in multidimensional Euclidean space and solve it using standard probabilistic tools such as the LLN and the Central Limit Theorem (CLT).

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来源期刊

American Statistician 数学-统计学与概率论

CiteScore

3.50

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： Are you looking for general-interest articles about current national and international statistical problems and programs; interesting and fun articles of a general nature about statistics and its applications; or the teaching of statistics? Then you are looking for The American Statistician (TAS), published quarterly by the American Statistical Association. TAS contains timely articles organized into the following sections: Statistical Practice, General, Teacher''s Corner, History Corner, Interdisciplinary, Statistical Computing and Graphics, Reviews of Books and Teaching Materials, and Letters to the Editor.