Dynamical Gibbs-non-Gibbs transitions for finite-alphabet models on trees

[2608.14802] Dynamical Gibbs-non-Gibbs transitions for finite-alphabet models on trees Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2608.14802 (math) [Submitted on 14 Aug 2026] Title: Dynamical Gibbs-non-Gibbs transitions for finite-alphabet models on trees Authors: Sebastian Bergmann , Christof Külske , Niklas Schubert View a PDF of the paper titled Dynamical Gibbs-non-Gibbs transitions for finite-alphabet models on trees, by Sebastian Bergmann and 2 other authors View PDF HTML (experimental) Abstract: We study finite-alphabet spin models on trees evolving under independent symmetric spin-flip dynamics. On the lattice the time-evolved plus measure of the low temperature Ising model in zero external field was shown to be non-quasilocal for all sufficiently large times in \cite{EnFeHoRe02}. On the tree however the time-evolved plus phase of the Ising model behaves differently, as the quasilocal Gibbs property is first lost, but then recovered at a later time \cite{EnErIaKu12}. We first extend this result by showing that large-time reentry into the quasilocal Gibbs regime on the tree happens more generally for all finite alphabet models, when the dynamics is started in $f$-stable Gibbs states. These are defined in terms of a time-independent sharp condition on the homogeneous recursion $f$ describing the model, which can be checked explicitly. As our second and opposite result, we develop a method for proving large-time persistence of non-quasilocality of time-evolved measures. We show that even all configurations can become bad at large times, when the initial Gibbs measure corresponds to an $f$-saddle and give an explicit illustration for the Potts model. In our proofs we study the influence of spatially inhomogeneous perturbations to the solutions of a time-dependent fixed point problem. Comments: 33 pages, 4 figures, 2 tables Subjects: Probability (math.PR) ; Mathematical Physics (math-ph) MSC classes: 82B26 (Primary) 60K35 (Secondary) ACM classes: G.3 Cite as: arXiv:2608.14802 [math.PR] (or arXiv:2608.14802v1 [math.PR] for this version) https://doi.org/10.48550/arXiv.2608.14802 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Niklas Schubert [ view email ] [v1] Fri, 14 Aug 2026 18:15:28 UTC (905 KB) Full-text links: Access Paper: View a PDF of the paper titled Dynamical Gibbs-non-Gibbs transitions for finite-alphabet models on trees, by Sebastian Bergmann and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2026-08 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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