Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications (London Mathematical Society Lecture Note Series, Series Number 389)

Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical random fields. The main emphasis is on tools from harmonic analysis, beginning with the representation theory for the group of rotations SO(3). Many recent developments on the method of moments and cumulants for the analysis of Gaussian subordinated fields are reviewed. This background material is used to analyse spectral representations of isotropic spherical random fields and then to investigate in depth the properties of associated harmonic coefficients. Properties and statistical estimation of angular power spectra and polyspectra are addressed in full. The authors are strongly motivated by cosmological applications, especially the analysis of cosmic microwave background (CMB) radiation data, which has initiated a challenging new field of mathematical and statistical research. Ideal for mathematicians and statisticians interested in applications to cosmology, it will also interest cosmologists and mathematicians working in group representations, stochastic calculus and spherical wavelets.

Domenico Marinucci is a Full Professor of Probability and Mathematical Statistics and Director of the Department of Mathematics at the University of Rome, 'Tor Vergata'. He is also a Core Team member for the ESA satellite experiment 'Planck'.

Giovanni Peccati is Full Professor in Stochastic Analysis at the University of Luxembourg.