On the Multiplicative Chaos of Non-Gaussian Log-Correlated Fields

Abstract

Abstract 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.