{"paper":{"title":"Directed polymers in heavy-tail random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Niccolo Torri, Quentin Berger","submitted_at":"2018-02-09T17:09:05Z","abstract_excerpt":"We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\\alpha\\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse temperature temperature $\\beta=\\beta_n$ vanishes as the size of the system $n$ goes to infinity. When $\\alpha\\in(1/2,2)$, we show that all possible transversal fluctuations $\\sqrt{n} \\leq h_n \\leq n$ can be achieved by tuning properly $\\beta_n$, allowing to interpolate between all super-diffusive scales. Moreover, we determine the scaling limit of the model, ans"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03355","kind":"arxiv","version":2},"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"}