Random Fields on the Sphere
Representation, Limit Theorems and Cosmological Applications
Published on 25. August 2011
Book
Paperback/Softback
356 pages
978-0-521-17561-6 (ISBN)
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.
Reviews / Votes
"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
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises; 2 Halftones, unspecified; 10 Line drawings, unspecified
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 21 mm
Weight
575 gr
ISBN-13
978-0-521-17561-6 (9780521175616)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Domenico Marinucci | Giovanni Peccati
Random Fields on the Sphere
Representation, Limit Theorems and Cosmological Applications
E-Book
12/2011
1st Edition
Cambridge University Press
€82.99
Available for download
Persons
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.
Content
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.