{"paper":{"title":"Gap metrics for stationary point processes and quantitative convexity of the free energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bastian M\\\"uller, Martin Huesmann","submitted_at":"2025-09-10T14:53:47Z","abstract_excerpt":"In this article, we are interested in convexity properties of the free energy for stationary point processes on $\\mathbb R$ w.r.t.\\ a new geometry inspired by optimal transport. We will show for a rich class of pairwise interaction energies\n  A) quantified strict convexity of the free energy implying uniqueness of minimizers\n  B) existence of a gradient flow curve of the free energy w.r.t. the new metric converging exponentially fast to the unique minimizer.\n  Examples for energies for which A holds include logarithmic or Riesz interactions with parameter $0<s<1$, examples for which A and B ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08659","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/2509.08659/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"}