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A probabilistic approach to the geometry of the ℓᵨⁿ-ball

Barthe, Franck; Guedon, Olivier; Mendelson, Shahar; Naor, Assaf


This article investigates, by probabilistic methods, various geometric questions on Bᵨⁿ, the unit ball of ℓᵨⁿ. We propose realizations in terms of independent random variables of several distributions on Bᵨⁿ, including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in Bᵨⁿ. As another application, we compute moments of linear functionals on Bᵨⁿ, which gives sharp constants in Khinchine’s inequalities...[Show more]

CollectionsANU Research Publications
Date published: 2005-03-29
Type: Journal article
Source: Annals of Probability
DOI: 10.1214/009117904000000874


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