2026-07-25T01:58:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20000 2024-06-06T06:21:15Z ddc:004 open_access

Dimensionality of Hamming Metrics and Rademacher Type Eskenazis, Alexandros Hamming cube Rademacher type metric embeddings Borsuk-Ulam theorem Let X be a finite-dimensional normed space. We prove that if the Hamming cube {-1,1}ⁿ embeds into X with bi-Lipschitz distortion at most D ≥ 1, then dim(X) ≳ sup_{p ∈ [1,2]} n^p/(D^p 𝖳_p(X)^p), where 𝖳_p(X) is the Rademacher type p constant of X. This estimate yields a mutual refinement of distortion lower bounds which follow from works of Oleszkiewicz (1996) and Ivanisvili, van Handel and Volberg (2020). The proof relies on a combination of semigroup techniques on the biased hypercube with the Borsuk-Ulam theorem from algebraic topology. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alexandros Eskenazis 2024 Is Part Of LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2024.55 urn:nbn:de:0030-drops-200004 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.55 eng https://creativecommons.org/licenses/by/4.0/legalcode