{"paper":{"title":"From optimal transportation to optimal teleportation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gershon Wolansky","submitted_at":"2014-02-17T13:12:54Z","abstract_excerpt":"The object of this paper is to study estimates of $\\epsilon^{-q}W_p(\\mu+\\epsilon\\nu, \\mu)$ for small $\\epsilon>0$. Here $W_p$ is the Wasserstein metric on positive measures, $p>1$, $\\mu$ is a probability measure and $\\nu$ a signed, neutral measure ($\\int d\\nu=0$). In [W1] we proved uniform (in $\\epsilon$) estimates for $q=1$ provided $\\int \\phi d\\nu$ can be controlled in terms of the $\\int|\\nabla\\phi|^{p/(p-1)}d\\mu$, for any smooth function $\\phi$.\n  In this paper we extend the results to the case where such a control fails. This is the case where if, e.g. $\\mu$ has a disconnected support, or "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3990","kind":"arxiv","version":5},"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"}