Hydrodynamic limit for an evolutional model of two-dimensional Young diagrams

[0909.5482] Hydrodynamic limit for an evolutional model of two-dimensional Young diagrams Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:0909.5482 (math) [Submitted on 30 Sep 2009] Title: Hydrodynamic limit for an evolutional model of two-dimensional Young diagrams Authors: Tadahisa Funaki , Makiko Sasada View a PDF of the paper titled Hydrodynamic limit for an evolutional model of two-dimensional Young diagrams, by Tadahisa Funaki and Makiko Sasada View PDF HTML (experimental) Abstract: We construct dynamics of two-dimensional Young diagrams, which are naturally associated with their grandcanonical ensembles, by allowing the creation and annihilation of unit squares located at the boundary of the diagrams. The grandcanonical ensembles, which were introduced by Vershik, are uniform measures under conditioning on their size (or equivalently, area). We then show that, as the averaged size of the diagrams diverges, the corresponding height variable converges to a solution of a certain non-linear partial differential equation under a proper hydrodynamic scaling. Furthermore, the stationary solution of the limit equation is identified with the so-called Vershik curve. We discuss both uniform and restricted uniform statistics for the Young diagrams. Comments: 29 pages Subjects: Probability (math.PR) ; Mathematical Physics (math-ph) MSC classes: 60K35, 82C22 Cite as: arXiv:0909.5482 [math.PR] (or arXiv:0909.5482v1 [math.PR] for this version) https://doi.org/10.48550/arXiv.0909.5482 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Commun. Math. Phys. 299, 335-363 (2010) Related DOI : https://doi.org/10.1007/s00220-010-1082-z Focus to learn more DOI(s) linking to related resources Submission history From: Tadahisa Funaki [ view email ] [v1] Wed, 30 Sep 2009 01:48:08 UTC (25 KB) Full-text links: Access Paper: View a PDF of the paper titled Hydrodynamic limit for an evolutional model of two-dimensional Young diagrams, by Tadahisa Funaki and Makiko Sasada View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2009-09 Change to browse by: math math-ph math.MP 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

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