Skip to content
University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • A. James Clark School of Engineering
    • Institute for Systems Research Technical Reports
    • View Item
    •   DRUM
    • A. James Clark School of Engineering
    • Institute for Systems Research Technical Reports
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

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

    Thumbnail
    View/Open
    HanMakowskiUniformFinal.pdf (343.2Kb)
    No. of downloads: 1227

    Date
    2008-10-24
    Author
    Han, Guang
    Makowski, Armand M.
    Advisor
    Makowski, Armand M.
    Metadata
    Show full item record
    Abstract
    Consider 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.
    URI
    http://hdl.handle.net/1903/8665
    Collections
    • Institute for Systems Research Technical Reports

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility