{"paper":{"title":"Edgeworth-type expansion for the one-point distribution of the KPZ fixed point with a large height at a prior location","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ron Nissim, Ruixuan Zhang","submitted_at":"2022-10-10T20:05:27Z","abstract_excerpt":"We consider the Kardar-Parisi-Zhang (KPZ) fixed point $\\mathrm{H}(x,\\tau)$ with the narrow-wedge initial condition and investigate the distribution of $\\mathrm{H}(x,\\tau)$ conditioned on a large height at an earlier space-time point $\\mathrm{H}(x',\\tau')$. As $\\mathrm{H}(x',\\tau')$ tends to infinity, we prove that the conditional one-point distribution of $\\mathrm{H}(x,\\tau)$ in the regime $\\tau>\\tau'$ converges to the Gaussian Unitary Ensemble (GUE) Tracy-Widom distribution and that the next two lower-order error terms can be expressed as derivatives of the Tracy-Widom distribution. The lowe "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.04999","kind":"arxiv","version":6},"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/2210.04999/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"}