{"paper":{"title":"Optimal transportation and pressure at zero temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.DS","authors_text":"Jairo K. Mengue","submitted_at":"2025-01-31T18:21:10Z","abstract_excerpt":"Given two compact metric spaces $X$ and $Y$, a Lipschitz continuous cost function $c$ on $X \\times Y$ and two probabilities $\\mu \\in\\mathcal{P}(X),\\,\\nu\\in\\mathcal{P}(Y)$, we propose to study the Monge-Kantorovich problem and its duality from a zero temperature limit of a convex pressure function. We consider the entropy defined by $H(\\pi) = -D_{KL}(\\pi|\\mu\\times \\nu)$, where $D_{KL}$ is the Kullback-Leibler divergence, and then the pressure defined by the variational principle \\[P(\\beta A) = \\sup_{\\pi \\in \\Pi(\\mu,\\nu)} \\left[ \\smallint \\beta A\\,d\\pi + H(\\pi)\\right],\\]where $\\beta>0$ and $A=-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19369","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.19369/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}