Duality between box-ball systems of finite box and/or carrier capacity

[1905.00189] Duality between box-ball systems of finite box and/or carrier capacity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:1905.00189 (math) [Submitted on 1 May 2019] Title: Duality between box-ball systems of finite box and/or carrier capacity Authors: David A. Croydon , Makiko Sasada View a PDF of the paper titled Duality between box-ball systems of finite box and/or carrier capacity, by David A. Croydon and 1 other authors View PDF HTML (experimental) Abstract: We construct the dynamics of the box-ball system with box capacity $J$ and carrier capacity $K$, which we abbreviate to BBS($J$,$K$), in the case of infinite initial configurations, and show that this system is dual to the analogous BBS($K$,$J$) model. Towards this end, we build on previous work for the original box-ball system, that is BBS($1$,$\infty$), to show that when the box capacity $J$ and carrier capacity $K$ satisfy $J<K$ the dynamics can be represented by a Pitman-type transformation. These ideas are applied in the case of random initial configurations to show that the distributional properties of spatial stationarity and invariance under the BBS dynamics are dual. Moreover, for independent and identically distributed configurations, we derive a characterisation of invariant measures in terms of a detailed balance equation, which captures the duality of the system locally; this is used to find all invariant measures in this class. Finally, we deduce the speed of a tagged particle, and show that this also satisfies a natural duality relation. Subjects: Probability (math.PR) ; Mathematical Physics (math-ph) MSC classes: 37B15 (primary), 60G50, 60K35, 82B99 (secondary) Cite as: arXiv:1905.00189 [math.PR] (or arXiv:1905.00189v1 [math.PR] for this version) https://doi.org/10.48550/arXiv.1905.00189 Focus to learn more arXiv-issued DOI via DataCite Journal reference: RIMS Kokyuroku Bessatsu 79(2020) Submission history From: David Croydon [ view email ] [v1] Wed, 1 May 2019 05:30:20 UTC (55 KB) Full-text links: Access Paper: View a PDF of the paper titled Duality between box-ball systems of finite box and/or carrier capacity, by David A. Croydon and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2019-05 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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