Research Paper#Probability, High-Dimensional Geometry, Statistics🔬 ResearchAnalyzed: Jan 3, 2026 15:36
Limit Theorems for Distances in $l_p^n$-Balls
Published:Dec 30, 2025 17:25
•1 min read
•ArXiv
Analysis
This paper investigates the statistical properties of the Euclidean distance between random points within and on the boundaries of $l_p^n$-balls. The core contribution is proving a central limit theorem for these distances as the dimension grows, extending previous results and providing large deviation principles for specific cases. This is relevant to understanding the geometry of high-dimensional spaces and has potential applications in areas like machine learning and data analysis where high-dimensional data is common.
Key Takeaways
Reference
“The paper proves a central limit theorem for the Euclidean distance between two independent random vectors uniformly distributed on $l_p^n$-balls.”