• Login
    JavaScript is disabled for your browser. Some features of this site may not work without it.
    Random Structures 
    •   QMRO Home
    • Queen Mary University of London Theses
    • Theses
    • Random Structures
    •   QMRO Home
    • Queen Mary University of London Theses
    • Theses
    • Random Structures
    ‌
    ‌

    Browse

    All of QMROCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects
    ‌
    ‌

    Administrators only

    Login
    ‌
    ‌

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Random Structures

    Publisher
    Queen Mary University of London
    Metadata
    Show full item record
    Abstract
    For many combinatorial objects we can associate a natural probability distribution on the members of the class, and we can then call the resulting class a class of random structures. Random structures form good models of many real world problems, in particular real networks and disordered media. For many such problems, the systems under consideration can be very large, and we often care about whether a property holds most of the time. In particular, for a given class of random structures, we say that a property holds with high probability if the probability that that property holds tends to one as the size of the structures increase. We examine several classes of random structures with real world applications, and look at some properties of each that hold with high probability. First we look at percolation in 3 dimensional lattices, giving a method for producing rigorous confidence intervals on the percolation threshold. Next we look at random geometric graphs, first examining the connectivity thresholds of nearest neighbour models, giving good bounds on the threshold for a new variation on these models useful for modelling wireless networks, and then look at the cop number of the Gilbert model. Finally we look at the structure of random sum-free sets, in particular examining what the possible densities of such sets are, what substructures they can contain, and what superstructures they belong to.
    Authors
    Ball, Neville
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/7902
    Collections
    • Theses [3833]
    Copyright statements
    The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author
    Twitter iconFollow QMUL on Twitter
    Twitter iconFollow QM Research
    Online on twitter
    Facebook iconLike us on Facebook
    • Site Map
    • Privacy and cookies
    • Disclaimer
    • Accessibility
    • Contacts
    • Intranet
    • Current students

    Modern Slavery Statement

    Queen Mary University of London
    Mile End Road
    London E1 4NS
    Tel: +44 (0)20 7882 5555

    © Queen Mary University of London.