Connectivity in one-dimensional geometric random graphs: Poisson approximations, zero-one laws and phase transitions

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dc.contributor.advisorMakowski, Armand M.
dc.contributor.authorHan, Guang
dc.contributor.authorMakowski, Armand M.
dc.date.accessioned2008-11-07T21:19:01Z
dc.date.available2008-11-07T21:19:01Z
dc.date.issued2008-10-24
dc.description.abstractConsider n points (or nodes) distributed uniformly and independently on the unit interval [0,1]. Two nodes are said to be adjacent if their distance is less than some given threshold value.For the underlying random graph we derive zero-one laws for the property of graph connectivity and give the asymptotics of the transition widths for the associated phase transition. These results all flow from a single convergence statement for the probability of graph connectivity under a particular class of scalings. Given the importance of this result, we give two separate proofs; one approach relies on results concerning maximal spacings, while the other one exploits a Poisson convergence result for the number of breakpoint users.en
dc.description.sponsorshipThis work was prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011.en
dc.format.extent351457 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/8665
dc.language.isoen
dc.relation.isAvailableAtInstitute for Systems Researchen_us
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_us
dc.relation.isAvailableAtUniversity of Maryland (College Park, MD)en_us
dc.relation.ispartofseriesTR_2008-30en
dc.subjectGeometric random graphsen
dc.subjectConnectivityen
dc.subjectZero-one lawsen
dc.subjectCritical scalingsen
dc.subjectPhase transitionsen
dc.titleConnectivity in one-dimensional geometric random graphs: Poisson approximations, zero-one laws and phase transitionsen
dc.typeArticleen

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