{"paper":{"title":"Nonlinear noise excitation of intermittent stochastic PDEs and the topology of LCA groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Kunwoo Kim","submitted_at":"2013-02-13T22:40:34Z","abstract_excerpt":"Consider the stochastic heat equation $\\partial_tu=\\mathscr{L}u+\\lambda\\sigma(u)\\xi$, where $\\mathscr{L}$ denotes the generator of a L\\'{e}vy process on a locally compact Hausdorff Abelian group $G$, $\\sigma:\\mathbf{R}\\to\\mathbf{R}$ is Lipschitz continuous, $\\lambda\\gg1$ is a large parameter, and $\\xi$ denotes space-time white noise on $\\mathbf{R}_+\\times G$. The main result of this paper contains a near-dichotomy for the (expected squared) energy $\\mathrm{E}(\\|u_t\\|_{L^2(G)}^2)$ of the solution. Roughly speaking, that dichotomy says that, in all known cases where $u$ is intermittent, the ener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3266","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"}