{"paper":{"title":"A Boundedness Trichotomy for the Stochastic Heat Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Kunwoo Kim, Le Chen","submitted_at":"2015-10-15T19:28:14Z","abstract_excerpt":"We consider the stochastic heat equation with a multiplicative white noise forcing term under standard \"intermitency conditions.\" The main finding of this paper is that, under mild regularity hypotheses, the a.s.-boundedness of the solution $x\\mapsto u(t\\,,x)$ can be characterized generically by the decay rate, at $\\pm\\infty$, of the initial function $u_0$. More specifically, we prove that there are 3 generic boundedness regimes, depending on the numerical value of $\\Lambda:= \\lim_{|x|\\to\\infty} |\\log u_0(x)|/(\\log|x|)^{2/3}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04674","kind":"arxiv","version":1},"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"}