Random Fields on the Sphere
Representation, Limit Theorems and Cosmological Applications

Reviews recent developments in the analysis of isotropic spherical random fields, with a view towards applications in cosmology.

Domenico Marinucci (Author), Giovanni Peccati (Author)

9780521175616, Cambridge University Press

Paperback, published 25 August 2011

356 pages, 12 b/w illus.
22.8 x 15.3 x 1.9 cm, 0.52 kg

"The methods described in the book shed light on extremely important issues in astrophysics, cosmology, and fundamental physics. Most of the results of the book were first proved by the authors. Rigourous mathematical proofs of other results appear here for the first time in a monograph form. ...the material is very accessible, both technically interesting and a pleasure to read. The presentation is very clear. The book is a must for mathematicians and for graduate and postgraduate students who would like to work in the area of statistical analysis of cosmological data."
Anatoliy Malyarenko, Mathematical Reviews

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.

Preface
1. Introduction
2. Background results in representation theory
3. Representations of SO(3) and harmonic analysis on S2
4. Background results in probability and graphical methods
5. Spectral representations
6. Characterizations of isotropy
7. Limit theorems for Gaussian subordinated random fields
8. Asymptotics for the sample power spectrum
9. Asymptotics for sample bispectra
10. Spherical needlets and their asymptotic properties
11. Needlets estimation of power spectrum and bispectrum
12. Spin random fields
Appendix
Bibliography
Index.

Subject Areas: Cosmology & the universe [PGK], Stochastics [PBWL], Probability & statistics [PBT]