{"paper":{"title":"Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension","license":"","headline":"","cross_cats":["cond-mat.soft","nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"A.A. Masoudi, F. Shahbazi, J. Davoudi, M. Reza Rahimi Tabar","submitted_at":"2001-06-05T13:42:13Z","abstract_excerpt":"The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops sharply connected valley structures within which the height derivative {\\it is not} continuous. There are two different regimes before and after creation of the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1 dimension driven with a random forcing which is white in time and Gaussian correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient $P(h-\\bar h,\\partial_{x}h,t)$ when the forcing correlation length is much smal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0106076","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"}