This paper presents necessary and sufficient conditions for the peakedness comparison and convex ordering between two elliptically contoured random fields about their centers. A somewhat surprising finding is that the peakedness comparison for the infinite dimensional case differs from the finite dimensional case. For example, a Student’s t distribution is known to be more heavy-tailed than a normal distribution, but a Student’s t random field and a Gaussian random field are not comparable in terms of the peakedness. In particular, the peakedness comparison and convex ordering are made for isotropic elliptically contoured random fields on compact two-point homogeneous spaces.

中文翻译：

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椭圆轮廓随机场的随机比较

本文提出了两个椭圆轮廓随机场围绕其中心进行峰值比较和凸排序的充要条件。一个有点令人惊讶的发现是，无限维情况的峰值比较与有限维情况不同。例如，已知学生 t 分布比正态分布更重尾，但学生 t 随机场和高斯随机场在峰值方面不可比。特别是，对紧凑两点齐次空间上的各向同性椭圆轮廓随机场进行了峰值比较和凸排序。