{"paper":{"title":"Simple derivation of the $(- \\lambda H)^{5/2}$ tail for the 1D KPZ equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexandre Krajenbrink, Pierre Le Doussal","submitted_at":"2018-02-23T16:08:19Z","abstract_excerpt":"We study the long-time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions for the Brownian and droplet initial conditions and present a simple derivation of the tail of the large deviations of the height on the negative side $\\lambda H<0$. We show that for both initial conditions, the cumulative distribution functions take a large deviations form, with a tail for $- \\tilde s \\gg 1$ given by $-\\log \\mathbb{P}\\left(\\frac{H}{t}<\\tilde{s}\\right)=t^2 \\frac{4 }{15 \\pi} (-\\tilde{s})^{5/2} $. This exact expression was already observed at small time for both initial conditions suggest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08618","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"}