{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hyperuniform-and-rigid-stable-matchings","title":"Hyperuniform and rigid stable matchings","arxiv_id":"1810.00265","date":"2018-09-29","proceeding":null,"authors":["Michael Andreas Klatt","Günter Last","D. Yogeshwaran"],"abstract":"We study a stable partial matching $\\tau$ of the (possibly randomized) $d$-dimensional lattice with a stationary determinantal point process $\\Psi$ on $\\mathbb{R}^d$ with intensity $\\alpha>1$. For instance, $\\Psi$ might be a Poisson process. The matched points from $\\Psi$ form a stationary and ergodic (under lattice shifts) point process $\\Psi^\\tau$ with intensity $1$ that very much resembles $\\Psi$ for $\\alpha$ close to $1$. On the other hand $\\Psi^\\tau$ is hyperuniform and number rigid, quite in contrast to a Poisson process. We deduce these properties by proving more general results for a stationary point process $\\Psi$, whose so-called matching flower (a stopping set determining the matching partner of a lattice point) has a certain subexponential tail behaviour. For hyperuniformity, we also additionally need to assume some mixing condition on $\\Psi$. Further, if $\\Psi$ is a Poisson process then $\\Psi^\\tau$ has an exponentially decreasing truncated pair correlation function.","url_abs":"http://arxiv.org/abs/1810.00265v3","url_pdf":"http://arxiv.org/pdf/1810.00265v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"hyperuniform-and-rigid-stable-matchings","repo_url":"https://github.com/michael-klatt/matchingpp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}