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dc.contributor.authorDavis, Erik
dc.contributor.authorSethuraman, Sunder
dc.date.accessioned2019-06-14T22:59:27Z
dc.date.available2019-06-14T22:59:27Z
dc.date.issued2019-06
dc.identifier.citationDavis, Erik; Sethuraman, Sunder. Approximating geodesics via random points. Ann. Appl. Probab. 29 (2019), no. 3, 1446--1486. doi:10.1214/18-AAP1414. https://projecteuclid.org/euclid.aoap/1550566835en_US
dc.identifier.issn1050-5164
dc.identifier.doi10.1214/18-AAP1414
dc.identifier.urihttp://hdl.handle.net/10150/632900
dc.description.abstractGiven a cost functional F on paths gamma in a domain D subset of R-d, in the form 1 F(gamma) = integral(1)(0) f (gamma(t), gamma(t)) dt , it is of interest to approximate its minimum cost and geodesic paths. Let X-1,...X-n be points drawn independently from D according to a distribution with a density. Form a random geometric graph on the points where X-i and X-j are connected when 0 < vertical bar X-i - X-j vertical bar < epsilon, and the length scale epsilon = epsilon(n) vanishes at a suitable rate. For a general class of functionals F, associated to Finsler and other distances on D, using a probabilistic form of Gamma convergence, we show that the minimum costs and geodesic paths, with respect to types of approximating discrete cost functionals, built from the random geometric graph, converge almost surely in various senses to those corresponding to the continuum cost F, as the number of sample points diverges. In particular, the geodesic path convergence shown appears to be among the first results of its kind.en_US
dc.description.sponsorshipARO [W911NF-18-1-0311]; Simons sabbatical granten_US
dc.language.isoenen_US
dc.publisherINST MATHEMATICAL STATISTICSen_US
dc.relation.urlhttps://projecteuclid.org/euclid.aoap/1550566835en_US
dc.rights© Institute of Mathematical Statistics, 2019.en_US
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectGeodesicen_US
dc.subjectshortest pathen_US
dc.subjectdistanceen_US
dc.subjectconsistencyen_US
dc.subjectrandom geometric graphen_US
dc.subjectGamma convergenceen_US
dc.subjectscaling limiten_US
dc.subjectFinsleren_US
dc.titleApproximating geodesics via random pointsen_US
dc.typeArticleen_US
dc.contributor.departmentUniv Arizona, Dept Mathen_US
dc.identifier.journalANNALS OF APPLIED PROBABILITYen_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal published versionen_US
dc.source.journaltitleThe Annals of Applied Probability
dc.source.volume29
dc.source.issue3
dc.source.beginpage1446
dc.source.endpage1486
refterms.dateFOA2019-06-14T22:59:28Z


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