We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the corresponding spectral measure are needed to enter the set. One sees different decay rates in “different directions”, illustrating the phenomenon of hidden regular variation. We give several examples and obtain quite varied behavior, including sets which do not have exact power-law decay.

中文翻译：

---

对称稳定分布的隐藏正则变化行为公式

我们针对对称稳定随机向量的各种集合的幂律衰减，开发了一个公式，以计算从相应频谱量度的支持中需要进入的向量数量。人们在“不同方向”上看到不同的衰减率，这说明了隐藏的规则变化现象。我们给出几个例子，并获得相当多的行为，包括没有精确幂律衰减的集合。