[2002.09459] Hidden invariance of last passage percolation and directed polymers Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2002.09459 (math) [Submitted on 21 Feb 2020 ( v1 ), last revised 30 Apr 2026 (this version, v5)] Title: Hidden invariance of last passage percolation and directed polymers Authors: Duncan Dauvergne View a PDF of the paper titled Hidden invariance of last passage percolation and directed polymers, by Duncan Dauvergne View PDF HTML (experimental) Abstract: Last passage percolation and directed polymer models on $\mathbb Z^2$ are invariant under translation and certain reflections. When these models have an integrable structure coming from either the RSK correspondence or the geometric RSK correspondence (e.g. geometric last passage percolation or the log-gamma polymer), we show that these basic invariances can be combined with a decoupling property to yield a rich new set of symmetries. Among other results, we prove shift and rearrangement invariance statements for last passage times, geodesic locations, disjointness probabilities, polymer partition functions, and quenched polymer measures. We also use our framework to find `scrambled' versions of the classical RSK correspondence, and to find an RSK correspondence for moon polyominoes. The results extend to limiting models, including the KPZ equation and the Airy sheet. Comments: 45 pages, 10 figures. v5 update: The proof of Theorem 3.3 in v4 (and in the published Ann. Probab. version) had a gap in the case when m < n. The proof has been expanded in v5 to address this case Subjects: Probability (math.PR) ; Combinatorics (math.CO) MSC classes: Primary: 60K35, Secondary: 05A15, 05A19, 05E10 Cite as: arXiv:2002.09459 [math.PR] (or arXiv:2002.09459v5 [math.PR] for this version) https://doi.org/10.48550/arXiv.2002.09459 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Duncan Dauvergne [ view email ] [v1] Fri, 21 Feb 2020 18:25:09 UTC (159 KB) [v2] Thu, 27 Feb 2020 18:27:13 UTC (159 KB) [v3] Tue, 26 May 2020 19:42:40 UTC (446 KB) [v4] Thu, 28 Oct 2021 15:49:11 UTC (453 KB) [v5] Thu, 30 Apr 2026 21:36:13 UTC (477 KB) Full-text links: Access Paper: View a PDF of the paper titled Hidden invariance of last passage percolation and directed polymers, by Duncan Dauvergne View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2020-02 Change to browse by: math math.CO References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from