{"paper":{"title":"Precise asymptotics for the parabolic Anderson model with a moving catalyst or trap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adrian Schnitzler, Tilman Wolff","submitted_at":"2010-10-07T18:59:49Z","abstract_excerpt":"We consider the solution $u\\colon [0,\\infty) \\times\\mathbb{Z}^d\\rightarrow [0,\\infty) $ to the parabolic Anderson model, where the potential is given by $(t,x)\\mapsto\\gamma\\delta_{Y_t}(x)$ with $Y$ a simple symmetric random walk on $\\mathbb{Z}^d$. Depending on the parameter $\\gamma\\in[-\\infty,\\infty)$, the potential is interpreted as a randomly moving catalyst or trap. In the trap case, i.e., $\\gamma<0$, we look at the annealed time asymptotics in terms of the first moment of $u$. Given a localized initial condition, we derive the asymptotic rate of decay to zero in dimensions 1 and 2 up to eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1512","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"}