Network exploration by random walks: A large deviation perspective

[2604.20829] Network exploration by random walks: A large deviation perspective Skip to main content Search Submit Donate Log in Physics > Physics and Society arXiv:2604.20829 (physics) [Submitted on 22 Apr 2026 ( v1 ), last revised 23 Apr 2026 (this version, v2)] Title: Network exploration by random walks: A large deviation perspective Authors: Sarvesh K. Upadhyay , Trifce Sandev , Sanjay Kumar , R. K. Singh View PDF HTML (experimental) Abstract: We study exploration properties of a random walk on a network. For a fully connected network we find that the problem can be mapped to the well known coupon collector problem, thus allowing us to estimate form of $P(S,t)$: the distribution of number of distinct nodes $S$ visited by the random walk upto time $t$. From a practical point of view, however, both the fully connected network and hops taking place after fixed intervals are an idealization. We solve this problem by introducing the formalism of continuous time random walks wherein the random walk spends a random amount of time a node before hopping to its neighboring node. The formalism allows us to study the large deviation limit of $P(S,t)$ under very mild conditions that the distribution of waiting times $\psi(\tau)$ exhibits analyticity at small times. Furthermore, we find that at small times, the properties of $P(S,t)$ are largely independent of the network topology, and are governed solely by the waiting time characteristics. Comments: 10 pages, 5 Figures Subjects: Physics and Society (physics.soc-ph) Cite as: arXiv:2604.20829 [physics.soc-ph] (or arXiv:2604.20829v2 [physics.soc-ph] for this version) https://doi.org/10.48550/arXiv.2604.20829 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Chaos, Solitons & Fractals 211, 118810 (2026) Related DOI : https://doi.org/10.1016/j.chaos.2026.118810 Focus to learn more DOI(s) linking to related resources Submission history From: Sarvesh K. Upadhyay [ view email ] [v1] Wed, 22 Apr 2026 17:56:26 UTC (1,511 KB) [v2] Thu, 23 Apr 2026 14:08:42 UTC (1,511 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: physics.soc-ph < prev | next > new | recent | 2026-04 Change to browse by: physics References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

Related documents

• Network exploration by random walks: A large deviation perspective#670569
• Network Accuracy Across Levels of Analysis Using Stochastic Block Models#233215
• Network Accuracy Across Levels of Analysis Using Stochastic Block Models#16259
• Large deviations for random sums and random convex polygons#326181
• Large-deviations theory for growing chemical reaction networks#1105529