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Title: Thresholds in probabilistic and extremal combinatorics
Author: Falgas-Ravry, Victor
ISNI:       0000 0004 2734 3628
Awarding Body: Queen Mary University of London
Current Institution: Queen Mary, University of London
Date of Award: 2012
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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.
Supervisor: Not available Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Combinatorics ; Discrete structures ; Probabilistic combinatorics ; Extremal combinatorics