In this article we study the tail probability of the mass of Gaussian multiplicative chaos. With the novel use of a Tauberian argument and Goldie’s implicit renewal theorem, we provide a unified approach to general log-correlated Gaussian fields in arbitrary dimension and derive precise first order asymptotics of the tail probability, resolving a conjecture of Rhodes and Vargas. The leading order is described by a universal constant that captures the generic property of Gaussian multiplicative chaos, and may be seen as the analogue of the Liouville unit volume reflection coefficients in higher dimensions.

中文翻译：

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高斯乘法混沌的通用尾部轮廓

在本文中，我们研究了高斯乘法混沌质量的尾部概率。通过 Tauberian 论证和 Goldie 隐式更新定理的新颖使用，我们为任意维度的一般对数相关高斯场提供了一种统一的方法，并推导出尾概率的精确一阶渐近，解决了 Rhodes 和 Vargas 的猜想。领先阶数由一个通用常数描述，该常数捕捉了高斯乘法混沌的通用属性，可以看作是高维中刘维尔单位体积反射系数的类似物。