High Dimensional Space Oddity
Probability
2025-01-24 v2 Statistics Theory
Statistics Theory
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).
Cite
@article{arxiv.2409.13046,
title = {High Dimensional Space Oddity},
author = {Haim Bar and Vladimir Pozdnyakov},
journal= {arXiv preprint arXiv:2409.13046},
year = {2025}
}
Comments
16 pages, 3 figures