非高斯各向同性场的角谱
Angular Spectra for non-Gaussian Isotropic Fields
摘要：
宇宙微波背景辐射各向异性是多个科学领域的研究热点之一。本文从CMB的应用出发，对统计学的基本概念和理论进行了系统的阐述。本文的主要结果是非高斯光场按谱各向同性的充要条件。明确的公式，双，三，和多谱和双，三，和更高的顺序协方差。关键词：双谱，三谱，角多谱，宇宙微波背景辐射;高斯性;球面随机场
英文摘要：
Cosmic Microwave Background (CMB) Anisotropies is a subject of intensive research in several fields of sciences. In this paper we start a systematic development of basic notions and theory in statistics according to the application for CMB. The main result of this paper is the necessary and sufficient condition for isotropy of a non-Gaussian field in terms of spectra. Clear formulae for bi-, tri- and polyspectra and bi-, tri-, and higher order covariances are also given. Keywords: Bispectrum, Trispectrum, Angular poly-Spectra, Cosmic microwave background radiation; Gaussianity; spherical random fields
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