{"paper":{"title":"Quenched central limit theorem for the stochastic heat equation in weak disorder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chiranjib Mukherjee, Yannic Broeker","submitted_at":"2017-10-02T13:35:28Z","abstract_excerpt":"We continue with the study of the mollified stochastic heat equation in $d\\geq 3$ given by $d u_{\\epsilon,t}=\\frac 12\\Delta u_{\\epsilon,t}+ \\beta \\epsilon^{(d-2)/2} \\,u_{\\epsilon,t} \\,d B_{\\epsilon,t}$ with spatially smoothened cylindrical Wiener process $B$, whose (renormalized) Feynman-Kac solution describes the partition function of the continuous directed polymer. In an earlier work (\\cite{MSZ16}), a phase transition was obtained, depending on the value of $\\beta>0$ in the limiting object of the smoothened solution $u_\\epsilon$ as the smoothing parameter $\\epsilon\\to 0$ This partition func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00631","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"}