{"paper":{"title":"Quenched Lyapunov exponent for the parabolic Anderson model in a dynamic random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank den Hollander, Gr\\'egory Maillard, J\\\"urgen G\\\"artner","submitted_at":"2010-11-02T08:44:44Z","abstract_excerpt":"We continue our study of the parabolic Anderson equation $\\partial u/\\partial t = \\kappa\\Delta u + \\gamma\\xi u$ for the space-time field $u\\colon\\,\\Z^d\\times [0,\\infty)\\to\\R$, where $\\kappa \\in [0,\\infty)$ is the diffusion constant, $\\Delta$ is the discrete Laplacian, $\\gamma\\in (0,\\infty)$ is the coupling constant, 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\" $\\xi$, both living on $\\Z^d$. In earlier work we considered three c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0541","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"}