Correlations between Maxwell's multipoles for Gaussian random functions on the sphere

Journal of Physics A: Mathematical and General

Volumn 38, Issue 8, 2005, Pages 1653-1658

  Dennis, M R ^a,b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14544298831     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/8/002     Document Type: Article

References (22)

1. Maxwell J C 1891 A Treatise on Electricity and Magnetism vol l, 3rd edn (Oxford: Clarendon Press reprinted by Dover, 1954)
2. Sylvester J J 1876 Note on spherical harmonics Phil. Mag. 2 291-307 Sylvester J J 1909 The Collected Mathematical Papers of James Joseph Sylvester vol 3 (Cambridge: Cambridge University Press)
3. Sylvester J J 1876 Note on spherical harmonics Phil. Mag. 2 291-307 Sylvester J J 1909 The Collected Mathematical Papers of James Joseph Sylvester vol 3 (Cambridge: Cambridge University Press)
4. Courant R and Hilbert D 1953 Methods of Mathematical Physics vol 1 (New York: Interscience Publishers)
5. Dennis M R 2004 Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere J. Phys. A: Math. Gen. 37 9487-500
6. Copi C J, Huterer D and Starkman G D 2004 Multipole vectors: A new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2 ≤ ℓ ≤ 8 Phys. Rev. D 70 043515
7. Schwartz D J, Starkman G D, Huterer D and Copi C J 2004 Is the low-ℓ microwave background cosmic? Phys. Rev. Lett. 93 221301
8. Land K and Magueijo J 2004 Multipole invariants and non-Gaussianity Preprint astro-ph/0407081
9. Majorana E 1932 Atomi orientati in campo magnetico variabile Nuovo. Cimento 9 43-50
10. Bacry H 1974 Orbits of the rotation group on spin states J. Math. Phys. 15 1686-8
11. Penrose R 2004 The Road to Reality (London: Jonathan Cape)
12. Hannay J H 1996 Chaotic analytic zero points: exact statistics for a random spin state J. Phys. A: Math. Gen. 29 L101-5
13. Bogomolny E, Bohigas O and Leboeuf P 1992 Distribution of roots of random polynomials Phys. Rev. Lett. 68 2726-9
14. Prosen T 1996 Exact statistics of complex zeros for Gaussian random polynomials with real coefficients J. Phys. A: Math. Gen. 29 4417-23
15. Bogomolny E, Bohigas O and Leboeuf P 1996 Quantum chaotic dynamics and random polynomials J. Stat. Phys. 85 639-79
16. Braun D, Kuś M and Życzkowski K 1997 Time-reversal symmetry and random polynomials J. Phys. A: Math. Gen. 30 L117-23
17. Hannay J H 1998 The chaotic analytic function J. Phys. A: Math. Gen. 31 L755-61
18. Lebœuf P 1999 Random analytic chaotic eigenstates J. Stat. Phys. 95 651-64
19. Forrester P J and Honner G 1999 Exact statistical properties of the zeros of complex random polynomials J. Phys. A: Math. Gen. 32 2961-81
20. Bleher P, Shiffman B and Zelditch S 2000 Universality and scaling between zeros on complex manifolds Invent. Math. 142 351-95
21. Dennis M R 2003 Correlations and screening of topological charges in Gaussian random fields J. Phys. A : Math. Gen. 36 6611-28
22. Caillol J M 1981 Exact results for a two-dimensional one-component plasma J. Phys. Lett. - Paris 42 L245-7