{"paper":{"title":"Anderson polymer in a fractional Brownian environment: asymptotic behavior of the partition function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frederi G. Viens, Kamran Kalbasi, Thomas S. Mountford","submitted_at":"2016-02-17T17:16:52Z","abstract_excerpt":"We consider the Anderson polymer partition function $$ u(t):=\\mathbb{E}^X\\Bigl[e^{\\int_0^t \\mathrm{d}B^{X(s)}_s}\\Bigr]\\,, $$ where $\\{B^{x}_t\\,;\\, t\\geq0\\}_{x\\in\\mathbb{Z}^d}$ is a family of independent fractional Brownian motions all with Hurst parameter $H\\in(0,1)$, and $\\{X(t)\\}_{t\\in \\mathbb{R}^{\\geq 0}}$ is a continuous-time simple symmetric random walk on $\\mathbb{Z}^d$ with jump rate $\\kappa$ and started from the origin. $\\mathbb{E}^X$ is the expectation with respect to this random walk.\n  We prove that when $H\\leq 1/2$, the function $u(t)$ almost surely grows asymptotically like $e^{l "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05491","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"}