Representations of SO(3) and angular polyspectra

Journal of Multivariate Analysis

Volumn 101, Issue 1, 2010, Pages 77-100

  Marinucci, D ^a   Peccati, G ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Group representations; Isotropy; Polyspectra; Spherical random fields

Indexed keywords

EID: 70350101172     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2009.04.017     Document Type: Article

References (38)

1. Diaconis P. Group Representations in Probability and Statistics. IMS Lecture Notes-Monograph Series vol. 11 (1988), Hayward, California
2. Bump D. Lie Groups (2004), Springer-Verlag, Berlin, Heidelberg, New York
3. Diaconis P., Mayer-Wolf E., Zeitouni O., and Zerner M. The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations. The Annals of Probability 32 1B (2004) 915-938
4. Fulman J. Convergence rates of random walk on irreducible representations of finite groups. Journal of Theoretical Probability 21 (2008) 193-211
5. Guivarc'h Y., Keane M., and Roynette B. Marches Aléatoires sul les Groupes de Lie. Lecture Notes in Mathematics vol. 624 (1977), Springer-Verlag
6. J.-R. Pycke, A decomposition for invariant tests of uniformity on the sphere, Proceedings of the American Mathematical Society (2007) (in press)
7. Raimond O. Flots browniens isotropes sur la sph ère. Annales de l'institut Henri Poincaré (B) Probabilité s et Statistiques 35 3 (1999) 313-354
8. Yadrenko M.I. Spectral Theory of Random Fields (1983), Optimization Software, Inc., New York
9. G. Peccati, J.-R. Pycke, Decompositions of stochastic processes based on irreducible group representations, Theory of Probability and its Applications (2005) (in press)
10. Marinucci D., and Peccati G. High-frequency asymptotics for subordinated stationary fields on an Abelian compact group. Stochastic Processes and their Applications 118 (2008) 585-613
11. D. Marinucci, G. Peccati, Group representations and high-resolution central limit theorems for subordinated spherical random fields, 2008, Preprint. arXiv:0706.2851
12. Varshalovich D.A., Moskalev A.N., and Khersonskii V.K. Quantum Theory of Angular Momentum (1988), World Scientific Press
13. Vilenkin N.Ja., and Klimyk A.U. Representation of Lie Groups and Special Functions (1991), Kluwer, Dordrecht
14. Cabella P., and Marinucci D. Statistical Challenges in the Analysis of Cosmic Microwave Background. The Annals of Applied Statistics 3 1 (2009)
15. Dodelson S. Modern Cosmology (2003), Academic Press
16. Hu W. The angular trispectrum of the CMB. Physical Review D 64 (2001) id. 083005
17. Komatsu E., and Spergel D.N. Acoustic signatures in the primary microwave background bispectrum. Physical Review D 63 (2001) id. 063002
18. Marinucci D. High-resolution asymptotics for the angular bispectrum of spherical random fields. The Annals of Statistics 34 (2006) 1-41
19. Marinucci D. A central limit theorem and higher order results for the angular bispectrum. Probability Theory and Related Fields 141 (2007) 389-409
20. N L with WMAP data. Monthly Notices of the Royal Astronomical Society 369 (2006) 819-824
21. N L) in the WMAP 3-year data at above 99.5% confidence, 2007. arxiv:0712.1148
22. A.P.S. Yadav, E. Komatsu, B.D. Wandelt, M. Liguori, F.K. Hansen, S. Matarrese, Fast estimator of primordial Non-Gaussianity from temperature and polarization anisotropies in the cosmic microwave background II: Partial sky coverage and inhomogeneous noise, 2007, Preprint. arXiv:0711.4933
23. Babich D., Creminelli P., and Zaldarriaga M. The Shape of non-Gaussianities. Journal of Cosmology and Astroparticle Physics 8 (2004) 009
24. Bartolo N., Komatsu E., Matarrese S., and Riotto A. Non-Gaussianity from inflation: Theory and observations. Physical Reports 402 (2004) 103-266
25. Maldacena J. Non-Gaussian features of primordial fluctuations in single field inflationary models. Journal of High Energy Physics 5 (2003) 0-13
26. Chung M.K., Dalton K.M., Evans A.C., and Davidson R.J. Tensor-based cortical surface morphometry via weighted spherical harmonics representation. IEEE Transactions on Medical Imaging (2007)
27. Simons F.J., Dahlen F.A., and Wieczorek M.A. Spatiospectral concentration on a sphere. SIAM Review 48 3 (2006) 504-536
28. Wieczorek M.A., and Simons F.J. Minimum-variance multitaper spectral estimation on the sphere. The Journal of Fourier Analysis and Applications 13 6 (2007) 665-692
29. Adler R.J., and Taylor J.E. Random Fields and Geometry (2007), Springer
30. Baldi P., and Marinucci D. Some characterizations of the spherical harmonics coefficients for isotropic random fields. Statistics and Probability Letters 77 5 (2007) 490-496
31. Baldi P., Marinucci D., and Varadarajan V.S. On the characterization of isotropic random fields on homogeneous spaces of compact groups. Electronic Communications in Probability 12 (2007) 291-302
32. D. Geller, D. Marinucci, Spin wavelets on the sphere, 2008, Preprint. arXiv:0811.2935
33. Liboff R.L. Introductory Quantum Mechanics (1999), Addison-Wesley
34. Stanley R.P. Enumerative Combinatorics, vol. I (1997), Cambridge University Press
35. Biedenharn L.C., and Louck J.D. The Racah-Wigner Algebra in Quantum Theory. Encyclopaedia of Mathematics and its Applications vol. 10 (1981), Addison-Wesley
36. Surgailis D. CLTs for polynomials of linear sequences: Diagram formula with illustrations. Theory and Applications of Long Range Dependence (2003), Birkhäuser 111-128
37. Sagan B.E. The Symmetric Group. Representations, Combinatorial Algorithms and Symmetric Functions. 2nd ed. (2001), Springer-Verlag
38. Sternberg S. Group Theory and Physics (1999), Cambridge University Press