{"paper":{"title":"The localization transition for the directed polymer in a random environment is smooth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hubert Lacoin","submitted_at":"2025-05-19T17:25:15Z","abstract_excerpt":"When $d\\ge 3$, the directed polymer a in random environment on $\\mathbb Z^d$ is known to display a phase transition from a diffusive phase, known as \\textit{weak disorder} to a localized phase, referred to as \\textit{strong disorder}. This transition is encoded by the behavior of the the free energy of the model, defined by $$\\mathfrak f(\\beta):=\\lim_{N\\to \\infty} (1/n)\\log W^{\\beta}_n$$ where $W^{\\beta}_n$ is the normalized partition function for the directed polymer of length $n$. More precisely weak disorder corresponds to $\\mathfrak f(\\beta)=0$ and strong disorder to $\\mathfrak f(\\beta)<0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13382","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/2505.13382/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"}