The Lamperti transformation in the infinite-dimensional setting, self-similar populations, and coalescents

[2405.10193] The Lamperti transformation in the infinite-dimensional setting, self-similar populations, and coalescents Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2405.10193 (math) [Submitted on 16 May 2024 ( v1 ), last revised 13 Apr 2026 (this version, v4)] Title: The Lamperti transformation in the infinite-dimensional setting, self-similar populations, and coalescents Authors: Arno Siri-Jégousse , Alejandro Hernández Wences View a PDF of the paper titled The Lamperti transformation in the infinite-dimensional setting, self-similar populations, and coalescents, by Arno Siri-J\'egousse and Alejandro Hern\'andez Wences View PDF HTML (experimental) Abstract: We propose a change in focus from the prevalent paradigm based on the branching property as a tool to analyze the structure of population models, to one based on the self-similarity property, which we also introduce for the first time in the setting of measure-valued processes. By extending the well-known Lamperti transformation into the infinite dimensional setting, we were able to embed and extend known results in population genetics within the self-similarity framework: we describe the frequency process of a larger class of measure-valued SS populations in terms of general Lambda Fleming-Viot processes. Our results demonstrate the potential power of the self-similar perspective for the study of populations whose total size varies stochastically over time, and in which the reproduction dynamics of the individuals are not independent from one another but are modulated by the total size of the population, allowing for more complex and realistic models. We also uncover a new duality relation between measure-valued processes and Lambda-coalescents which extends the well-known duality relation between Lambda Fleming-Viot processes and Lambda coalescents. Subjects: Probability (math.PR) MSC classes: 92D25, 60G18, 60J68 Cite as: arXiv:2405.10193 [math.PR] (or arXiv:2405.10193v4 [math.PR] for this version) https://doi.org/10.48550/arXiv.2405.10193 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alejandro Hernández Wences [ view email ] [v1] Thu, 16 May 2024 15:37:19 UTC (76 KB) [v2] Mon, 27 May 2024 08:28:50 UTC (76 KB) [v3] Fri, 21 Mar 2025 14:56:50 UTC (83 KB) [v4] Mon, 13 Apr 2026 23:01:57 UTC (87 KB) Full-text links: Access Paper: View a PDF of the paper titled The Lamperti transformation in the infinite-dimensional setting, self-similar populations, and coalescents, by Arno Siri-J\'egousse and Alejandro Hern\'andez Wences View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2024-05 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

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