Random fields on the sphere
Subtitle: representation, limit theorems, and cosmological applications
By: Domenico Marinucci, Giovanni Peccati
Contributors: Peccati, Giovanni, 1975-
Series: London Mathematical Society lecture note series -- 389
Publisher: Cambridge University Press
Published: 2011
Place of publication: Cambridge; New York
Language: eng
Number of pages: 341
ISBN-13: 9780521175616
Subjects: Statistical methods; MATHEMATICS / Probability & Statistics / General; Random fields; Spherical harmonics; Compact groups; Cosmology
Description: "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 purpose of this monograph is to discuss recent developments in the analysis of isotropic spherical random fields, with a view towards applications in Cosmology.We shall be concerned in particular with the interplay among three leading themes, namely: - the connection between isotropy, representation of compact groups and spectral analysis for random fields, including the characterization of polyspectra and their statistical estimation - the interplay between Gaussianity, Gaussian subordination, nonlinear statistics, and recent developments in the methods of moments and diagram formulae to establish weak convergence results - the various facets of high-resolution asymptotics, including the high-frequency behaviour of Gaussian subordinated random fields and asymptotic statistics in the high-frequency sense"--
Table of contents: title: Machine generated contents note: 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.