High Dimensional Space Oddity

Haim Bar and Vladimir Pozdnyakov

The American Statistician, 2025, vol. 79, issue 4, 474-479

Abstract: 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).

Date: 2025
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DOI: 10.1080/00031305.2025.2505507

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