{"paper":{"title":"Asymptotic behavior of the stochastic heat equation over large intervals","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Candil, Marta Sanz Sol\\'e, Robert C. Dalang","submitted_at":"2025-09-02T16:55:18Z","abstract_excerpt":"We consider a nonlinear stochastic heat equation on $[0,T]\\times [-L,L]$, driven by a space-time white noise $W$, with a given initial condition $u_0: \\mathbb{R} \\to \\mathbb{R}$ and three different types of (vanishing) boundary conditions: Dirichlet, Mixed and Neumann. We prove that as $L\\to\\infty$, the random field solution at any space-time position converges in the $L^p(\\Omega)$-norm ($p\\ge 1$) to the solution of the stochastic heat equation on $\\mathbb{R}$ (with the same initial condition $u_0$), and we determine the (near optimal) rate of convergence. The proof relies on estimates of diff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02504","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.02504/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}