{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/synchronization-for-kpz","title":"Synchronization for KPZ","arxiv_id":"1907.06278","date":"2019-07-14","proceeding":null,"authors":["Tommaso Cornelis Rosati"],"abstract":"We study the longtime behavior of KPZ-like equations: $$ \\partial_{t}h(t,x) = \\Delta_{x} h (t, x) + | \\nabla_{x}h (t,x)|^{2} + \\eta(t, x), \\qquad h(0, x) = h_0(x), \\qquad (t, x) \\in (0, \\infty) \\times \\mathbb{T}^{d} $$ on the $d-$dimensional torus $\\mathbb{T}^{d}$ driven by an ergodic noise $\\eta$ (e.g. space-time white in $d= 1$. The analysis builds on infinite-dimensional extensions of similar results for positive random matrices. We establish a one force, one solution principle and derive almost sure synchronization with exponential deterministic speed in appropriate H\\\"older spaces.","url_abs":"https://arxiv.org/abs/1907.06278v3","url_pdf":"https://arxiv.org/pdf/1907.06278v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"synchronization-for-kpz","repo_url":"https://github.com/rosati-tom/SPDE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"synchronization-for-kpz","repo_url":"https://github.com/rosati-tom/Simulation-of-some-SPDEs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}