Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting

[2507.05800] Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Statistical Mechanics arXiv:2507.05800 (cond-mat) [Submitted on 8 Jul 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting Authors: Giuseppe Del Vecchio Del Vecchio , Manas Kulkarni , Satya N. Majumdar , Sanjib Sabhapandit View a PDF of the paper titled Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting, by Giuseppe Del Vecchio Del Vecchio and 3 other authors View PDF HTML (experimental) Abstract: We introduce \emph{proxitaxis}, a simple search strategy where the searcher has only information about the distance from the target but not the direction. The strategy consists of three crucial components: (i) local adaptive moves with distance-dependent hopping rate, (ii) intermittent long range returns via stochastic resetting to a certain location $\vec{R}_0$, and (iii) an inspection move where the searcher dynamically updates the resetting position $\vec{R}_0$. We compute analytically the capture probability of the target within this strategy and show that it can be maximized by an optimal choice of the control parameters of this strategy. Moreover, the optimal strategy undergoes multiple phase transitions as a function of the control parameters. These phase transitions are generic and occur in all dimensions. Comments: 5 pages, 7 figures, End Matters and Supplementary material included Subjects: Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2507.05800 [cond-mat.stat-mech] (or arXiv:2507.05800v2 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2507.05800 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. E 113, L042101 (2026) Related DOI : https://doi.org/10.1103/bjl2-kmrt Focus to learn more DOI(s) linking to related resources Submission history From: Giuseppe Del Vecchio Del Vecchio [ view email ] [v1] Tue, 8 Jul 2025 09:09:57 UTC (1,876 KB) [v2] Sat, 11 Apr 2026 11:11:02 UTC (2,077 KB) Full-text links: Access Paper: View a PDF of the paper titled Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting, by Giuseppe Del Vecchio Del Vecchio and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2025-07 Change to browse by: cond-mat 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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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