Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures

[1905.00186] Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:1905.00186 (math) [Submitted on 1 May 2019] Title: Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures Authors: David A. Croydon , Makiko Sasada View a PDF of the paper titled Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures, by David A. Croydon and 1 other authors View PDF HTML (experimental) Abstract: The box-ball system (BBS) is a simple model of soliton interaction introduced by Takahashi and Satsuma in the 1990s. Recent work of the authors, together with Tsuyoshi Kato and Satoshi Tsujimoto, derived various families of invariant measures for the BBS based on two-sided stationary Markov chains. In this article, we survey the invariant measures that were presented in the latter work, and also introduce a family of new ones for periodic configurations that are expressed in terms of Gibbs measures. Moreover, we show that the former examples can be obtained as infinite volume limits of the latter. Another aspect of the previous work was to describe scaling limits for the box-ball system; here, we review these results, and also present scaling limits other than those that were covered there. One, the zigzag process has previously been observed in the context of queuing; another, a periodic version of the zigzag process, is apparently novel. Furthermore, we demonstrate that certain Palm measures associated with the stationary and periodic versions of the zigzag process yield natural invariant measures for the dynamics of corresponding versions of the ultra-discrete Toda lattice. Subjects: Probability (math.PR) ; Mathematical Physics (math-ph) MSC classes: 37B15 (primary), 60G50, 60J10, 60J65, 82B99 (secondary) Cite as: arXiv:1905.00186 [math.PR] (or arXiv:1905.00186v1 [math.PR] for this version) https://doi.org/10.48550/arXiv.1905.00186 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Mathematical Physics, 60 083301 (2019) Related DOI : https://doi.org/10.1063/1.5095622 Focus to learn more DOI(s) linking to related resources Submission history From: David Croydon [ view email ] [v1] Wed, 1 May 2019 05:00:55 UTC (36 KB) Full-text links: Access Paper: View a PDF of the paper titled Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures, 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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