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High Dimensional Space Oddity

Author

Listed:
  • Haim Bar
  • Vladimir Pozdnyakov

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).

Suggested Citation

  • Haim Bar & Vladimir Pozdnyakov, 2025. "High Dimensional Space Oddity," The American Statistician, Taylor & Francis Journals, vol. 79(4), pages 474-479, October.
    • Handle: RePEc:taf:amstat:v:79:y:2025:i:4:p:474-479
    DOI: 10.1080/00031305.2025.2505507
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