No dimension reduction for doubling subsets of $\ell_q$ when $q>2$ revisited
| Autor: | Baudier, Florent P., Swieçicki, Krzysztof, Swift, Andrew |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We revisit the main results from \cites{BGN_SoCG14,BGN_SIAM15} and \cite{LafforgueNaor14_GD} about the impossibility of dimension reduction for doubling subsets of $\ell_q$ for $q>2$. We provide an alternative elementary proof of this impossibility result that combines the simplicity of the construction in \cites{BGN_SoCG14,BGN_SIAM15} with the generality of the approach in \cite{LafforgueNaor14_GD} (except for $L_1$ targets). One advantage of this different approach is that it can be naturally generalized to obtain embeddability obstructions into non-positively curved spaces or asymptotically uniformly convex Banach spaces. Comment: 17 pages, 1 figure |
| Databáze: | arXiv |
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