[2311.07146] Locality properties for discrete and continuum Widom--Rowlinson models in random environments Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2311.07146 (math) [Submitted on 13 Nov 2023 ( v1 ), last revised 24 Apr 2026 (this version, v2)] Title: Locality properties for discrete and continuum Widom--Rowlinson models in random environments Authors: Benedikt Jahnel , Christof Külske , Alexander Zass View a PDF of the paper titled Locality properties for discrete and continuum Widom--Rowlinson models in random environments, by Benedikt Jahnel and 2 other authors View PDF HTML (experimental) Abstract: We consider the Widom--Rowlinson model in which hard balls of two possible colors are constrained to a hard-core repulsion between particles of different colors, in quenched random environments. These random environments model spatially dependent preferences for the attachment of balls. We investigate the possibility to represent the joint process of environment and infinite-volume Widom--Rowlinson measure in terms of continuous (quasilocal) Papangelou intensities. We show that this is not always possible: In the case of the symmetric Widom-Rowlinson model on a non-percolating environment, we can explicitly construct a discontinuity coming from the environment. This is a new phenomenon for systems of continuous particles, but it can be understood as a continuous-space echo of a simpler non-locality phenomenon known to appear for the diluted Ising model (Griffiths singularity random field) on the lattice, as we explain in the course of the proof. Comments: Manuscript accepted for publication in Annals of Applied Probability. 26 pages, 8 figures Subjects: Probability (math.PR) MSC classes: 60K35 (Primary) 60G55, 60G60, 82B20, 82B21 (Secondary) Cite as: arXiv:2311.07146 [math.PR] (or arXiv:2311.07146v2 [math.PR] for this version) https://doi.org/10.48550/arXiv.2311.07146 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alexander Zass [ view email ] [v1] Mon, 13 Nov 2023 08:25:21 UTC (288 KB) [v2] Fri, 24 Apr 2026 07:21:06 UTC (284 KB) Full-text links: Access Paper: View a PDF of the paper titled Locality properties for discrete and continuum Widom--Rowlinson models in random environments, by Benedikt Jahnel and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2023-11 Change to browse by: math 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