论文标题
球形单层面和多重随机场的分析
Analysis of Spherical Monofractal and Multifractal Random Fields
论文作者
论文摘要
rényi函数在分析多型随机场中起着重要作用。对于球体上的随机字段，文献中有三个模型明确知道了rényi函数。本文的理论部分介绍了球体上的多重分段随机字段，并开发了可以明确计算rényi函数的特定模型。然后将这些结果应用于普朗克任务收集的宇宙微波背景辐射数据。用于描述文献中这些数据的主要统计模型是各向同性高斯领域。我们介绍了基于模拟随机字段，计算Rényi函数以及用于不同场景和实际CMB数据的多重型频谱的数值多纹理研究和方法。
The Rényi function plays an important role in the analysis of multifractal random fields. For random fields on the sphere, there are three models in the literature where the Rényi function is known explicitly. The theoretical part of the article presents multifractal random fields on the sphere and develops specific models where the Rényi function can be computed explicitly. Then these results are applied to the Cosmic Microwave Background Radiation data collected from the Planck mission. The main statistical model used to describe these data in the literature is isotropic Gaussian fields. We present numerical multifractality studies and methodology based on simulating random fields, computing the Rényi function and the multifractal spectrum for different scenarios and actual CMB data.
