{"paper":{"title":"Parabolic Anderson model with a finite number of moving catalysts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabienne Castell, Gr\\'egory Maillard, Onur G\\\"un","submitted_at":"2010-10-23T10:15:53Z","abstract_excerpt":"We consider the parabolic Anderson model (PAM) which is given by the equation $\\partial u/\\partial t = \\kappa\\Delta u + \\xi u$ with $u\\colon\\, \\Z^d\\times [0,\\infty)\\to \\R$, where $\\kappa \\in [0,\\infty)$ is the diffusion constant, $\\Delta$ is the discrete Laplacian, and $\\xi\\colon\\,\\Z^d\\times [0,\\infty)\\to\\R$ is a space-time random environment that drives the equation. The solution of this equation describes the evolution of a \"reactant\" $u$ under the influence of a \"catalyst\" $\\xi$. In the present paper we focus on the case where $\\xi$ is a system of $n$ independent simple random walks each wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4868","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"}