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