Increasing domain asymptotics for the first Minkowski functional of spherical random fields

Leonenko, N.; Ruiz-Medina, M.

doi:10.1090/tpms/1053

Increasing domain asymptotics for the first Minkowski functional of spherical random fields

Authors: N. N. Leonenko and M. D. Ruiz-Medina
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 127-149
MSC (2010): Primary 60G60, 60F05, 60G10, 62E20
DOI: https://doi.org/10.1090/tpms/1053
Published electronically: February 21, 2019
MathSciNet review: 3746004
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Abstract: The restriction to the sphere of a homogeneous and isotropic random field defines a spherical isotropic random field. This paper derives central and noncentral limit results for the first Minkowski functional subordinated to homogeneous and isotropic Gaussian and chi-squared random fields, restricted to the sphere in $\mathbb{R}^{3}$ . Both scenarios are motivated by their interesting applications in the analysis of the Cosmic Microwave Background (CMB) radiation.

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