{"paper":{"title":"Snowflake universality of Wasserstein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Alexandr Andoni, Assaf Naor, Ofer Neiman","submitted_at":"2015-09-29T10:32:41Z","abstract_excerpt":"For $p\\in (1,\\infty)$ let $\\mathscr{P}_p(\\mathbb{R}^3)$ denote the metric space of all $p$-integrable Borel probability measures on $\\mathbb{R}^3$, equipped with the Wasserstein $p$ metric $\\mathsf{W}_p$. We prove that for every $\\varepsilon>0$, every $\\theta\\in (0,1/p]$ and every finite metric space $(X,d_X)$, the metric space $(X,d_{X}^{\\theta})$ embeds into $\\mathscr{P}_p(\\mathbb{R}^3)$ with distortion at most $1+\\varepsilon$. We show that this is sharp when $p\\in (1,2]$ in the sense that the exponent $1/p$ cannot be replaced by any larger number. In fact, for arbitrarily large $n\\in \\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08677","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}