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

Autore: Domenico Marinucci; Giovanni Peccati
Editore: Cambridge : Cambridge University Press, 2011.
Serie: London Mathematical Society Lecture Note Series, 389.
Edizione/Formato:   eBook : Document : EnglishVedi tutte le edizioni e i formati
Banca dati:WorldCat
Sommario:
Reviews recent developments in the analysis of isotropic spherical random fields, with a view towards applications in cosmology.
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Genere/forma: Electronic books
Informazioni aggiuntive sul formato: Print version:
Marinucci, Domenico.
Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications.
Cambridge : Cambridge University Press, ©2011
Tipo materiale: Document, Risorsa internet
Tipo documento: Internet Resource, Computer File
Tutti gli autori / Collaboratori: Domenico Marinucci; Giovanni Peccati
ISBN: 9781139117487 1139117483 1283296179 9781283296175 9780511751677 0511751672 9781139128148 1139128140 1139115316 9781139115315
Numero OCLC: 769341761
Note: 7.6.1 Convolutions as mixed states.
Descrizione: 1 online resource (355 pages).
Contenuti: Cover; Title; Copyright; Contents; Dedication; Preface; 1 Introduction; 1.1 Overview; 1.2 Cosmological motivations; 1.3 Mathematical framework; 1.4 Plan of the book; 2 Background Results in Representation Theory; 2.1 Introduction; 2.2 Preliminary remarks; 2.3 Groups: basic definitions; 2.3.1 First definitions and examples; 2.3.2 Cosets and quotients; 2.3.3 Actions; 2.4 Representations of compact groups; 2.4.1 Basic definitions; 2.4.2 Group representations and Schur Lemma; 2.4.3 Direct sum and tensor product representations; 2.4.4 Orthogonality relations; 2.5 The Peter-Weyl Theorem. 3 Representations of SO(3) and Harmonic Analysis on S23.1 Introduction; 3.2 Euler angles; 3.2.1 Euler angles for SU(2); 3.2.2 Euler angles for SO(3); 3.3 Wigner's D matrices; 3.3.1 A family of unitary representations of SU(2); 3.3.2 Expressions in terms of Euler angles and irreducibility; 3.3.3 Further properties; 3.3.4 The dual of SO(3); 3.4 Spherical harmonics and Fourier analysis on S2; 3.4.1 Spherical harmonics and Wigner's Dl matrices; 3.4.2 Some properties of spherical harmonics; 3.4.3 An alternative characterization of spherical harmonics; 3.5 The Clebsch-Gordan coefficients. 3.5.1 Clebsch-Gordan matrices3.5.2 Integrals of multiple spherical harmonics; 3.5.3 Wigner 3 j coefficients; 4 Background Results in Probability and Graphical Methods; 4.1 Introduction; 4.2 Brownian motion and stochastic calculus; 4.3 Moments, cumulants and diagram formulae; 4.4 The simplified method of moments on Wiener chaos; 4.4.1 Real kernels; 4.4.2 Further results on complex kernels; 4.5 The graphical method for Wigner coefficients; 4.5.1 From diagrams to graphs; 4.5.2 Further notation; 4.5.3 First example: sums of squares; 4.5.4 Cliques and Wigner 6 j coefficients. 4.5.5 Rule n. 1: loops are zero4.5.6 Rule n. 2: paired sums are one; 4.5.7 Rule n. 3: 2-loops can be cut, and leave a factor; 4.5.8 Rule n. 4: three-loops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic Peter-Weyl Theorem; 5.2.1 General statements; 5.2.2 Decompositions on the sphere; 5.3 Weakly stationary random fields in Rm; 5.4 Stationarity and weak isotropy in R3; 6 Characterizations of Isotropy; 6.1 Introduction; 6.2 First example: the cyclic group; 6.3 The spherical harmonics coefficients; 6.4 Group representations and polyspectra. 6.5 Angular polyspectra and the structure of?l1 ... ln6.5.1 Spectra of strongly isotropic fields; 6.5.2 The structure of?l1 ... ln; 6.6 Reduced polyspectra of arbitrary orders; 6.7 Some examples; 7 Limit Theorems for Gaussian Subordinated Random Fields; 7.1 Introduction; 7.2 First example: the circle; 7.3 Preliminaries on Gaussian-subordinated fields; 7.4 High-frequency CLTs; 7.4.1 Hermite subordination; 7.5 Convolutions and random walks; 7.5.1 Convolutions on?SO (3); 7.5.2 The cases q = 2 and q = 3; 7.5.3 The case of a general q: results and conjectures; 7.6 Further remarks.
Titolo della serie: London Mathematical Society Lecture Note Series, 389.
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Abstract:

Reviews recent developments in the analysis of isotropic spherical random fields, with a view towards applications in cosmology.  Per saperne di più…

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"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. Per saperne di più…

 
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