Thresholds in probabilistic and extremal combinatorics.
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, VictorCollections
- Theses [3711]