[2608.14450] Converse bounds for multiple graph alignment and correlation detection based on last matching Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Statistics Theory arXiv:2608.14450 (math) [Submitted on 14 Aug 2026] Title: Converse bounds for multiple graph alignment and correlation detection based on last matching Authors: Taha Ameen , Bruce Hajek View a PDF of the paper titled Converse bounds for multiple graph alignment and correlation detection based on last matching, by Taha Ameen and Bruce Hajek View PDF HTML (experimental) Abstract: The paper focuses on information theoretic converse bounds for the alignment of $m$ correlated graphs and for the detection of correlation among $m$ graphs. A simple idea for $m\geq 3$ is that if the alignment of $m-1$ of the graphs is revealed as extra information (by a genie for example) then it is still necessary to produce the alignment between the one remaining graph and the others, i.e. the last matching must be accomplished. For both Gaussian and Erdos-Renyi models, the last-matching problem is equivalent to one with two observed graphs, providing a path to extend converse bounds for $m=2$ to larger $m$. While the method is rather obvious for alignment, we show that the method can also be used to derive converse bounds for weak detection of correlation. Subjects: Statistics Theory (math.ST) ; Information Theory (cs.IT); Probability (math.PR) Cite as: arXiv:2608.14450 [math.ST] (or arXiv:2608.14450v1 [math.ST] for this version) https://doi.org/10.48550/arXiv.2608.14450 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Taha Ameen [ view email ] [v1] Fri, 14 Aug 2026 16:35:24 UTC (49 KB) Full-text links: Access Paper: View a PDF of the paper titled Converse bounds for multiple graph alignment and correlation detection based on last matching, by Taha Ameen and Bruce Hajek View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2026-08 Change to browse by: cs cs.IT math math.IT math.PR stat stat.TH 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