Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/25870
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dc.contributor.authorPenrose, MD-
dc.contributor.authorYang, X-
dc.date.accessioned2023-01-24T17:31:53Z-
dc.date.available2023-01-24T17:31:53Z-
dc.date.issued2023-01-06-
dc.identifierORCID iD: Xiaochuan Yang https://orcid.org/0000-0003-2435-4615-
dc.identifierhttps://arxiv.org/abs/2301.02506v1-
dc.identifier.citationPenrose, M.D. and Yang, X. (2023) 'Largest nearest-neighbour link and connectivity threshold in a polytopal random sample', arXiv:2301.02506v1 [math.PR], pp. 1 - 26. doi: 10.48550/arXiv.2301.02506.en_US
dc.identifier.urihttps://bura.brunel.ac.uk/handle/2438/25870-
dc.descriptionMaterial is not peer-reviewed by arXiv - the contents of arXiv submissions are wholly the responsibility of the submitter and are presented “as is” without any warranty or guarantee. By hosting works and other materials on this site, arXiv, Cornell University, and their agents do not in any way convey implied approval of the assumptions, methods, results, or conclusions of the work.en_US
dc.description.abstractCopyright © 2023 The Authors. Let $X_1,X_2, \ldots$ be independent identically distributed random points in a convex polytopal domain $A \subset \mathbb{R}^d$. Define the largest nearest neighbour link $L_n$ to be the smallest $r$ such that every point of $\mathcal X_n:=\{X_1,\ldots,X_n\}$ has another such point within distance $r$. We obtain a strong law of large numbers for $L_n$ in the large-$n$ limit. A related threshold, the connectivity threshold $M_n$, is the smallest $r$ such that the random geometric graph $G(\mathcal X_n, r)$ is connected. We show that as $n \to \infty$, almost surely $nL_n^d/\log n$ tends to a limit that depends on the geometry of $A$, and $nM_n^d/\log n$ tends to the same limit.en_US
dc.format.extent1 - 26-
dc.format.mediumElectronic-
dc.language.isoen_USen_US
dc.publisherCornell Universityen_US
dc.subjectprobabilityen_US
dc.subjectmath.PRen_US
dc.subject60D05en_US
dc.subject60F15en_US
dc.subject05C80en_US
dc.titleLargest nearest-neighbour link and connectivity threshold in a polytopal random sampleen_US
dc.typeArticleen_US
dc.identifier.doihttps://doi.org/10.48550/arXiv.2301.02506-
pubs.notes26 pages-
dc.identifier.eissn2331-8422-
dc.rights.holderThe Authors-
Appears in Collections:Dept of Mathematics Research Papers

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