论文标题
限制带限制球形随机场的游览区域的行为
Limiting Behavior for the Excursion Area of Band-Limited Spherical Random Fields
论文作者
论文摘要
在本文中，我们研究了一些限制限制的高斯和各向同性球体随机场的几何函数。我们的结果是基于Wiener混乱的扩展，用于高斯磁场的非线性变换和该场协方差函数的高频极限上的显式推导。作为简单的推论，我们还建立了游览区域的中心极限定理。
In this paper, we investigate some geometric functionals for band limited Gaussian and isotropic spherical random fields in dimension 2. In particular, we focus on the area of excursion sets, providing its behavior in the high energy limit. Our result is based on Wiener chaos expansion for non linear transform of Gaussian fields and on an explicit derivation on the high-frequency limit of the covariance function of the field. As a simple corollary we establish also the Central Limit Theorem for the excursion area.
