Theory of Probability and Mathematical Statistics
Increasing Domain Asymptotics for the First Minkowski Functional of Spherical Random Fields
N. N. Leonenko, M. D. Ruiz-Medina
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Abstract: The restriction to the sphere of an homogeneous and isotropic random field defines a spherical isotropic random field. This paper derives central and non-central limit results for the first Minkowski functional subordinated to homogeneous and isotropic Gaussian and chi-squared random fields, restricted to the sphere in R3. Both scenarios are motivated by their interesting applications in the analysis of the Cosmic Microwave Background (CMB) radiation.
Keywords: Central and non-central limit theorems, chi-squared random fields, Gaussian random fields, Karhunen-Loeve expansion, spherical Rosenblatt distribution
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