We study non-Gaussian log-correlated multiplicative chaos, where the random field is defined as a sum of independent fields that satisfy suitable moment and regularity conditions. The convergence, existence of moments and analyticity with respect to the inverse temperature are proven for the resulting chaos in the full subcritical range. These results are generalizations of the corresponding theorems for Gaussian multiplicative chaos. A basic example where our results apply is the non-Gaussian Fourier series \[\sum_{k=1}^\infty \frac{1}{\sqrt{k}}(A_k \cos(2\pi k x) + B_k \sin(2\pi k x)),\] where $A_k$ and $B_k$ are i.i.d. random variables.

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关于非高斯对数相关场的乘法混沌

我们研究非高斯对数相关乘法混沌，其中随机场被定义为满足合适矩和规律性条件的独立场的总和。对于在整个亚临界范围内产生的混沌，证明了关于逆温度的收敛性、矩的存在性和解析性。这些结果是高斯乘法混沌的相应定理的推广。我们的结果适用的一个基本例子是非高斯傅立叶级数 \[\sum_{k=1}^\infty \frac{1}{\sqrt{k}}(A_k \cos(2\pi kx) + B_k \sin(2\pi kx)),\] 其中 $A_k$ 和 $B_k$ 是 iid 随机变量。