{"paper":{"title":"Exact short-time height distribution in 1D KPZ equation and edge fermions at high temperature","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":"Alberto Rosso, Gregory Schehr, Pierre Le Doussal, Satya N. Majumdar","submitted_at":"2016-03-10T15:36:50Z","abstract_excerpt":"We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions in curved (or droplet) geometry. We show that for short time $t$, the probability distribution $P(H,t)$ of the height $H$ at a given point $x$ takes the scaling form $P(H,t) \\sim \\exp{\\left(-\\Phi_{\\rm drop}(H)/\\sqrt{t} \\right)}$ where the rate function $\\Phi_{\\rm drop}(H)$ is computed exactly. While it is Gaussian in the center, i.e., for small $H$, the PDF has highly asymmetric non-Gaussian tails which we characterize in detail. This function $\\Phi_{\\rm drop}(H)$ is surprisingly reminiscent of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03302","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"}