{"paper":{"title":"Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nicolas Perkowski, Willem van Zuijlen, Wolfgang K\\\"onig","submitted_at":"2020-09-24T11:40:20Z","abstract_excerpt":"We consider the parabolic Anderson model (PAM) $\\partial_t u = \\frac12 \\Delta u + \\xi u$ in $\\mathbb R^2$ with a Gaussian (space) white-noise potential $\\xi$. We prove that the almost-sure large-time asymptotic behaviour of the total mass at time $t$, written $U(t)$, is given by $\\log U(t)\\sim \\chi t \\log t$ for $t \\to \\infty$, with the deterministic constant $\\chi$ identified in terms of a variational formula. In earlier work of one of the authors this constant was used to describe the asymptotic behaviour $\\boldsymbol \\lambda_1(Q_t)\\sim\\chi\\log t$ of the principal eigenvalue $\\boldsymbol\\lam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11611","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"}