The Resource Random fields on the sphere : representation, limit theorems, and cosmological applications, Domenico Marinucci, Giovanni Peccati, (electronic resource)

Random fields on the sphere : representation, limit theorems, and cosmological applications, Domenico Marinucci, Giovanni Peccati, (electronic resource)

Label
Random fields on the sphere : representation, limit theorems, and cosmological applications
Title
Random fields on the sphere
Title remainder
representation, limit theorems, and cosmological applications
Statement of responsibility
Domenico Marinucci, Giovanni Peccati
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
"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"--
Member of
Assigning source
Provided by publisher
Cataloging source
MiAaPQ
http://library.link/vocab/creatorDate
1968-
http://library.link/vocab/creatorName
Marinucci, Domenico
Dewey number
523.101/5195
Index
no index present
Language note
English
LC call number
QA406
LC item number
.M37 2011
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorDate
1975-
http://library.link/vocab/relatedWorkOrContributorName
Peccati, Giovanni
Series statement
London Mathematical Society lecture note series
Series volume
389
http://library.link/vocab/subjectName
  • Spherical harmonics
  • Random fields
  • Compact groups
  • Cosmology
Label
Random fields on the sphere : representation, limit theorems, and cosmological applications, Domenico Marinucci, Giovanni Peccati, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • 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
  • 7.6.1 Convolutions as mixed states
Dimensions
unknown
Extent
1 online resource (355 p.)
Form of item
online
Isbn
9781139128148
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)2550000000055677
  • (EBL)775025
  • (OCoLC)769341761
  • (SSID)ssj0000555373
  • (PQKBManifestationID)11381454
  • (PQKBTitleCode)TC0000555373
  • (PQKBWorkID)10518310
  • (PQKB)10654385
  • (UkCbUP)CR9780511751677
  • (MiAaPQ)EBC775025
  • (EXLCZ)992550000000055677
Label
Random fields on the sphere : representation, limit theorems, and cosmological applications, Domenico Marinucci, Giovanni Peccati, (electronic resource)
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • 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
  • 7.6.1 Convolutions as mixed states
Dimensions
unknown
Extent
1 online resource (355 p.)
Form of item
online
Isbn
9781139128148
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)2550000000055677
  • (EBL)775025
  • (OCoLC)769341761
  • (SSID)ssj0000555373
  • (PQKBManifestationID)11381454
  • (PQKBTitleCode)TC0000555373
  • (PQKBWorkID)10518310
  • (PQKB)10654385
  • (UkCbUP)CR9780511751677
  • (MiAaPQ)EBC775025
  • (EXLCZ)992550000000055677

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