Random Fields on the Sphere

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

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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.show more

Product details

  • Electronic book text | 350 pages
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 12 b/w illus.
  • 1139119656
  • 9781139119658

About Domenico Marinucci

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.show more

Review quote

"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 Reviewsshow more

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.show more