{"paper":{"title":"Weak extinction versus global exponential growth of total mass for superdiffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Janos Englander, Renming Song, Yan-Xia Ren","submitted_at":"2013-01-29T06:50:48Z","abstract_excerpt":"Consider a superdiffusion $X$ on $\\mathbb R^d$ corresponding to the semilinear operator $\\mathcal{A}(u)=Lu+\\beta u-ku^2,$ where $L$ is a second order elliptic operator, $\\beta(\\cdot)$ is in the Kato class and bounded from above, and $k(\\cdot)\\ge 0$ is bounded on compact subsets of $\\R^d$ and is positive on a set of positive Lebesgue measure.\n  The main purpose of this paper is to complement the results obtained in \\cite{Englander:2004}, in the following sense. Let $\\lambda_\\infty $ be the $L^\\infty$-growth bound of the semigroup corresponding to the Schr\\\"odinger operator $L+\\beta $. If $\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6842","kind":"arxiv","version":3},"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"}