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  E-mail Message: I thought you might be interested in this item at http://58460.worldcat.org/oclc/768771958 Title: Random fields on the sphere : representation, limit theorems and cosmological applications Author: Domenico Marinucci; Giovanni Peccati Publisher: Cambridge, UK ; New York : Cambridge University Press, 2011. ISBN/ISSN: 9781139128148 1139128140 9780511751677 0511751672 1139115316 9781139115315 OCLC:768771958

  
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Subjects

• Spherical harmonics.
• Random fields.
• Compact groups.
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Random fields on the sphere : representation, limit theorems and cosmological applications

Author:	Domenico Marinucci; Giovanni Peccati
Publisher:	Cambridge, UK ; New York : Cambridge University Press, 2011.
Series:	London Mathematical Society lecture note series, 389.
Edition/Format:	eBook : Document : EnglishView all editions and formats
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"-- "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"--  Read more...