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Bibliographic Details
Main Authors: Alonso-Gutiérrez, David, Goñi, Javier Martín, Prochno, Joscha
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.24367
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Table of Contents:
  • In this paper, we prove that the Euclidean distance between two independent random vectors uniformly distributed on $l_p^n$-balls $(1 \leq p \leq \infty)$ or on its boundary satisfies a central limit theorem as $n$ tends to $\infty$. Also, we give a compact proof of the case of the sphere, which was proved by Hammersley. Furthermore, we complement our central limit theorem by providing large deviation principles for the cases $p \geq 2$.