{"paper":{"title":"On the global maximum of the solution to a stochastic heat equation with compact-support initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Mohammud Foondun","submitted_at":"2009-01-24T05:19:47Z","abstract_excerpt":"Consider a stochastic heat equation $\\partial_t u = \\kappa \\partial^2_{xx}u+\\sigma(u)\\dot{w}$ for a space-time white noise $\\dot{w}$ and a constant $\\kappa>0$. Under some suitable conditions on the the initial function $u_0$ and $\\sigma$, we show that the quantity \\limsup_{t\\to\\infty}t^{-1}\\ln\\E(\\sup_{x\\in\\R} |u_t(x)|^2) is bounded away from zero and infinity by explicit multiples of $1/\\kappa$. Our proof works by demonstrating quantitatively that the peaks of the stochastic process $x\\mapsto u_t(x)$ are highly concentrated for infinitely-many large values of $t$. In the special case of the pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3814","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"}