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    Thresholds in probabilistic and extremal combinatorics. 
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    Thresholds in probabilistic and extremal combinatorics.

    Publisher
    Queen Mary University of London
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    Abstract
    This thesis lies in the field of probabilistic and extremal combinatorics: we study discrete structures, with a focus on thresholds, when the behaviour of a structure changes from one mode into another. From a probabilistic perspective, we consider models for a random structure depending on some parameter. The questions we study are then: When (i.e. for what values of the parameter) does the probability of a given property go from being almost 0 to being almost 1? How do the models behave as this transition occurs? From an extremal perspective, we study classes of structures depending on some parameter. We are then interested in the following questions: When (for what value of the parameter) does a particular property become unavoidable? What do the extremal structures look like? The topics covered in this thesis are random geometric graphs, dependent percolation, extremal hypergraph theory and combinatorics in the hypercube.
    Authors
    Falgas-Ravry, Victor
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/8827
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    • Theses [3711]
    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
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