论文标题
一组渐近行为的渐近行为一组一组随机场
Asymptotic Behaviour of Level Sets of Needlet Random Fields
论文作者
论文摘要
我们考虑定义为加权平均形式的球形高斯征征的序列。我们的主要结果是在高能设置中的中心极限定理，对于其游览集的边界长度。该结果基于随机场非线性功能的Stein-Malliavin技术和Wiener混乱扩展。为此，对边界长度的每个混沌分量的方差进行了仔细的分析，这表明它们在标准化后，在膨胀的所有术语中均不稳定，并且没有前导组分。
We consider sequences of needlet random fields defined as weighted averaged forms of spherical Gaussian eigenfunctions. Our main result is a Central Limit Theorem in the high energy setting, for the boundary lengths of their excursion sets. This result is based on Stein-Malliavin techniques and Wiener chaos expansion for nonlinear functionals of random fields. To this end, a careful analysis of the variances of each chaotic component of the boundary length is carried out, showing that they are asymptotically constant, after normalisation, for all terms of the expansion and no leading component arises.
