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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.
Reference

“The paper proves a central limit theorem for the Euclidean distance between two independent random vectors uniformly distributed on $l_p^n$-balls.”

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Research Paper#Quantum Computing, Error Correction, Fracton Codes🔬 ResearchAnalyzed: Jan 3, 2026 19:28

Optimal Threshold and High Capacity of Fracton Codes

Published:Dec 28, 2025 11:36
1 min read
ArXiv

Analysis

This paper investigates the fault-tolerant properties of fracton codes, specifically the checkerboard code, a novel topological state of matter. It calculates the optimal code capacity, finding it to be the highest among known 3D codes and nearly saturating the theoretical limit. This suggests fracton codes are highly resilient quantum memory and validates duality techniques for analyzing complex quantum error-correcting codes.
Reference

“The optimal code capacity of the checkerboard code is $p_{th} \simeq 0.108(2)$, the highest among known three-dimensional codes.”

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