{"paper":{"title":"The intermediate disorder regime for a directed polymer model on a hierarchical lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeremy Clark, Sasa Kocic, Tom Alberts","submitted_at":"2015-08-19T20:47:06Z","abstract_excerpt":"We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number $b\\in \\mathbb{N}$ and a segment number $s\\in \\mathbb{N}$. When $b\\leq s$ previous work [27] has established that the model exhibits strong disorder for all positive values of the inverse temperature $\\beta$, and thus weak disorder reigns only for $\\beta=0$ (infinite temperature). Our focus is on the so-called intermediate disorder regime in which the inverse temperature $\\beta\\equiv \\beta_{n}$ vanishes at an appropriate rate "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04791","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":""},"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"}