An inverse problem for fractional random walks on finite graphs

[2408.05072] An inverse problem for fractional random walks on finite graphs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2408.05072 (math) [Submitted on 9 Aug 2024 ( v1 ), last revised 10 Apr 2026 (this version, v2)] Title: An inverse problem for fractional random walks on finite graphs Authors: Giovanni Covi , Matti Lassas View a PDF of the paper titled An inverse problem for fractional random walks on finite graphs, by Giovanni Covi and 1 other authors View PDF Abstract: We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial in the sense that they are limited to a fixed, observable subset B of X, while the random walk is fractional in the sense that it allows long jumps with a probability P decreasing as a fractional power of the distance along the graph. The transition probability P also depends on {\gamma}. We show that this kind of random walk data allows for the determination of a gauge class to which the transition probability matrix P belongs, which we discuss. Moreover, we show that if the transition probability matrix P is itself known, then the amount of vertices |X|, the edge set E and the conductivity {\gamma} (up to a positive factor) can be recovered. We also show a characterization of the random walk data in terms of the corresponding transition matrices P , which highlights a new surprising nonlocal property. This work is motivated by the recent strong interest in the study of the fractional Calderón problem in the Riemannian setting. Comments: 35 pages, 8 figures Subjects: Analysis of PDEs (math.AP) ; Probability (math.PR) MSC classes: 35R30, 26A33, 42B37, 46F12 Cite as: arXiv:2408.05072 [math.AP] (or arXiv:2408.05072v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2408.05072 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Giovanni Covi [ view email ] [v1] Fri, 9 Aug 2024 13:59:07 UTC (26 KB) [v2] Fri, 10 Apr 2026 06:50:14 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled An inverse problem for fractional random walks on finite graphs, by Giovanni Covi and 1 other authors View PDF TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2024-08 Change to browse by: math math.PR 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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