Real space methods for analyzing random fields, with applications to the cosmic microwave background

During the next few years a wealth of new cosmological data is expected to be released to the scientific community, and in particular the cosmic microwave background will be measured to a high precision. The scientific challenges are therefor expected to shift from producting experimental data, to be able to analyze these data. The goal of the project is to develop, implement and apply one set of such tools, based on so-called N-point correlation functions. These tools can be used to probe the statistical properties of any random field, and in particular determine whether or not the field is Gaussian. The main goal of studying Gaussianity in a CMB context is to be able to distinguish between different classes of cosmological models. Another is to check for systematics and foregrounds. While the CMB obviously is the main target of the current project, also other fields of science will gain from this work. The algorithms are general in philosophy and may be used on any two-dimensional random field. However, for some special cases, in par ticular that of a random field on a sphere, user-freindly software will be made publicly available.