Minkowski functionals in SO(3) for spin random fields

Pistolato Francesca, University of Luxembourg

In the present era, there is a growing interest in modeling data not only with scalar values but also with more sophisticated algebraic structures. An important example are spin spherical random fields, that can be defined as random sections of a bundle of the 2-sphere. These fields manifest in both gravitational lensing data and Cosmic Microwave Background polarization data, which can be seen as vectors on the complex plane. Motivated by studying anisotropies and divergence from Gaussianity of the latter, we study the excursion area over a certain level of their real part, computing the Lipschitz-Killing curvatures, geometric quantities that can be related to the so-called Minkowski functionals. Without requiring the isotropy of the field, one can explicit the dependence of such geometric quantities on the spin parameter and the level. Joint work with M. Stecconi.

Area: CS26 - Geometry of random fields (Michele Stecconi)

Keywords: Spin Random Fields, Lipschitz-Killing Curvatures, SO(3), spin weighted spherical harmonics

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