High Dimensional Space Oddity

Haim Bar; Vladimir Pozdnyakov

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arXiv · 2409.13046

High Dimensional Space Oddity

Haim Bar·Vladimir Pozdnyakov

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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).

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Haim Bar, Vladimir Pozdnyakov. 2024-09-19. High Dimensional Space Oddity. https://arxiv.org/abs/2409.13046

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