{"paper":{"title":"Sharp Quantitative Stability for the Pr\\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CO","math.MG","math.PR"],"primary_cat":"math.FA","authors_text":"Alessio Figalli, Marius Tiba, Peter van Hintum","submitted_at":"2025-01-08T18:09:25Z","abstract_excerpt":"The Borell-Brascamp-Lieb inequality is a classical extension of the Pr\\'ekopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The stability of these inequalities has received significant attention in recent years. Despite substantial progress in the geometric setting, a sharp quantitative stability result for the Pr\\'ekopa-Leindler inequality has remained elusive, even in the special case of log-concave functions. In this work, we provide a unified and definitive stability framework for these foundational inequalities. By establishing the optim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04656","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/2501.04656/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"}