Excursion sets of planar Gaussian fields - McAuley, M (2020)
Gaussian fields are widely used for modelling spatial phenomena in disciplines such as cosmology, medical imaging and quantum mechanics. Geometric properties of the excursion sets of such fields are well studied, as they provide important test statistics in these areas. There is also theoretical interest in the large scale topological behaviour of excursion sets of Gaussian fields, due to recent results suggesting a connection with discrete percolation models. In this thesis we study the geometry of planar Gaussian fields with a focus on one particular quantity; the number of excursion/level set components in a large domain, which is of interest both for statistical testing and in relation to percolation.