RECORD
Correlations between Maxwell's multipoles for gaussian random functions on the sphere
Mathematical Physics · Submitted 4 Oct 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In the limit of high $\ell,$ the 2-point function tends to a form previously derived by Hannay in the analogous problem for the Majorana sphere.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Maxwell's multipoles are a natural geometric characterisation of real functions on the sphere (with fixed $\ell$). The correlations between multipoles for gaussian random functions are calculated, by mapping the spherical functions to random polynomials. In the limit of high $\ell,$ the 2-point function tends to a form previously derived by Hannay in the analogous problem for the Majorana sphere. The application to the cosmic microwave background (CMB) is discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Maxwell's multipoles are a natural geometric characterisation of real functions on the sphere (with fixed $\ell$). | background 1.00 | 0.09 | 0.04 | asserted 1.00 |
| s1 | The correlations between multipoles for gaussian random functions are calculated, by mapping the spherical functions to random polynomials. | method 0.87 | 0.91 | 0.18 | asserted 1.00 |
| s2 | In the limit of high $\ell,$ the 2-point function tends to a form previously derived by Hannay in the analogous problem for the Majorana sphere. | result 1.00 | 0.70 | 0.40 | asserted 1.00 |
| s3 | The application to the cosmic microwave background (CMB) is discussed. | contribution 0.63 | 0.62 | 0.05 | asserted 0.76 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Maxwell's multipoles are a natural geometric characterisation of real functions on the sphere (with fixed $\ell$). The correlations between multipoles for gaussian random functions are calculated, by mapping the spherical functions to random polynomials. In the limit of high $\ell,$ the 2-point function tends to a form previously derived by Hannay in the analogous problem for the Majorana sphere. The application to the cosmic microwave background (CMB) is discussed.
Human review
References
How the literature uses it
3 arXiv papers cite this in 6 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
-
According to Maxwell's multipole vector decomposition of modes [ref] , we may write each eigenmode $f_ ℓ∈V^ℓ$ as [equation] where $r = √(x^2 + y^2 + z^2)$ and the decomposition is well defined up to flipping the signs of the direction vectors ${v_1,…,v_ℓ}$ and the scale factor, two at a time.
Orbifold construction of the modes of the Poincare dodecahedral space · Multipole vectors · 0.93
Cites it as background 1 paper
-
Dennis and Land attended to this question first in [ref] , followed up by [ref] .
Multipole vectors of completely random microwave skies for $l \leq 50$ · Statistical properties of multipole vectors · 0.95
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.