Random Fields on the Sphere
Random Fields on the Sphere
Giovanni Peccati, Université du Luxembourg
CAD$109.95
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.
- The first comprehensive treatment available
- Provides mathematical foundations for cosmological data analysis, especially CMB radiation
- Reviews the interaction between group representation theory, harmonic analysis on the sphere, isotropic random field and high frequency asymptotics
Reviews & endorsements
"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
Product details
October 2011Paperback
9780521175616
356 pages
228 × 153 × 19 mm
0.52kg
12 b/w illus.
Available
Table of Contents
- 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.
