Random fields on the sphere : representation, limit theorems and cosmological applications
 Author/Creator
 Marinucci, Domenico, 1968
 Language
 English.
 Imprint
 Cambridge ; New York, NY : Cambridge University Press, 2011.
 Physical description
 ix, 341 p. : ill. ; 23 cm.
 Series
 London Mathematical Society lecture note series ; 389.
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Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [326]337) and index.
 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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.
(source: Nielsen Book Data)  Supplemental links
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Bibliographic information
 Publication date
 2011
 Responsibility
 Domenico Marinucci, Giovanni Peccati.
 Series
 London Mathematical Society lecture note series ; 389
 Note
 "The London Mathematical Society"Cover.
 ISBN
 9780521175616 (pbk.)
 0521175615 (pbk.)