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Tensor Minkowski Functionals for random fields on the sphere

Chingangbam, Pravabati and Yogendran, KP and Joby, PK and Ganesan, Vidhya and Appleby, Stephen and Park, Changbom (2017) Tensor Minkowski Functionals for random fields on the sphere. In: JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS (12).

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Official URL: http://dx.doi.org/10.1088/1475-7516/2017/12/023

Abstract

We generalize the translation invariant tensor-valued Minkowski Functionals which are de fined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random field on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh fields. The results hold on flat as well as any curved space with affine connection. We elucidate the way in which the matrix elements encode information about the Gaussian nature and statistical isotropy (or departure from isotropy) of the field. Finally, we apply the method to maps of the Galactic foreground emissions from the 2015 PLANCK data and demonstrate their high level of statistical anisotropy and departure from Gaussianity.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the IOP PUBLISHING LTD, TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Depositing User: Id for Latest eprints
Date Deposited: 20 Jan 2018 06:04
Last Modified: 20 Jan 2018 06:04
URI: http://eprints.iisc.ac.in/id/eprint/58833

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