{"paper":{"title":"Subgaussian concentration and rates of convergence in directed polymers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kenneth S. Alexander, Nikos Zygouras","submitted_at":"2012-04-09T07:47:06Z","abstract_excerpt":"We consider directed random polymers in $(d+1)$ dimensions with nearly gamma i.i.d. disorder. We study the partition function $Z_{N,\\omega}$ and establish exponential concentration of $\\log Z_{N,\\omega}$ about its mean on the subgaussian scale $\\sqrt{N/\\log N}$ . This is used to show that $\\mathbb{E}[ \\log Z_{N,\\omega}]$ differs from $N$ times the free energy by an amount which is also subgaussian (i.e. $o(\\sqrt{N})$), specifically $O(\\sqrt{\\frac{N}{\\log N}}\\log \\log N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1819","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"}