{"paper":{"title":"Parabolic Anderson model with voter catalysts: dichotomy in the behavior of Lyapunov exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gr\\'egory Maillard, Samuel Sch\\\"opfer, Thomas Mountford","submitted_at":"2010-10-23T10:28:30Z","abstract_excerpt":"We consider the parabolic Anderson model $\\partial u/\\partial t = \\kappa\\Delta u + \\gamma\\xi u$ with $u\\colon\\, \\Z^d\\times R^+\\to \\R^+$, where $\\kappa\\in\\R^+$ is the diffusion constant, $\\Delta$ is the discrete Laplacian, $\\gamma\\in\\R^+$ is the coupling constant, and $\\xi\\colon\\,\\Z^d\\times \\R^+\\to\\{0,1\\}$ is the voter model starting from Bernoulli product measure $\\nu_{\\rho}$ with density $\\rho\\in (0,1)$. The solution of this equation describes the evolution of a \"reactant\" $u$ under the influence of a \"catalyst\" $\\xi$. In G\\\"artner, den Hollander and Maillard 2010 the behavior of the \\emph{an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4869","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"}