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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)
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The item Random fields on the sphere : representation, limit theorems, and cosmological applications, Domenico Marinucci, Giovanni Peccati, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Random fields on the sphere : representation, limit theorems, and cosmological applications, Domenico Marinucci, Giovanni Peccati, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 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 highresolution asymptotics, including the highfrequency behaviour of Gaussian subordinated random fields and asymptotic statistics in the highfrequency sense"
 Language

 eng
 eng
 Extent
 1 online resource (355 p.)
 Note
 Description based upon print version of record
 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 PeterWeyl 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 ClebschGordan coefficients
 3.5.1 ClebschGordan 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: 2loops can be cut, and leave a factor; 4.5.8 Rule n. 4: threeloops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic PeterWeyl 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 Gaussiansubordinated fields; 7.4 Highfrequency 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
 Isbn
 9781139128148
 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
 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 highresolution asymptotics, including the highfrequency behaviour of Gaussian subordinated random fields and asymptotic statistics in the highfrequency sense"
 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)
 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 PeterWeyl 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 ClebschGordan coefficients
 3.5.1 ClebschGordan 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: 2loops can be cut, and leave a factor; 4.5.8 Rule n. 4: threeloops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic PeterWeyl 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 Gaussiansubordinated fields; 7.4 Highfrequency 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)
 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 PeterWeyl 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 ClebschGordan coefficients
 3.5.1 ClebschGordan 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: 2loops can be cut, and leave a factor; 4.5.8 Rule n. 4: threeloops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic PeterWeyl 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 Gaussiansubordinated fields; 7.4 Highfrequency 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/Randomfieldsonthesphererepresentation/rAsZwR5YtKM/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/Randomfieldsonthesphererepresentation/rAsZwR5YtKM/">Random fields on the sphere : representation, limit theorems, and cosmological applications, Domenico Marinucci, Giovanni Peccati, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>