Absolute continuity of non-Gaussian and Gaussian multiplicative chaos measures
Abstract
In this article, we consider the multiplicative chaos measure associated to the log-correlated random Fourier series, or random wave model, with i.i.d. coefficients taken from a general class of distributions. This measure was shown to be non-degenerate when the inverse temperature is subcritical by Junnila (Int. Math. Res. Not. 2020 (2020), no. 19, 6169-6196). When the coefficients are Gaussian, this measure is an example of a Gaussian multiplicative chaos (GMC), a well-studied universal object in the study of log-correlated fields. In the case of non-Gaussian coefficients, the resulting chaos is not a GMC in general. However, we construct a coupling between the non-Gaussian multiplicative chaos measure and a GMC such that the two are almost surely mutually absolutely continuous.
Keywords
Cite
@article{arxiv.2410.19979,
title = {Absolute continuity of non-Gaussian and Gaussian multiplicative chaos measures},
author = {Yujin H. Kim and Xaver Kriechbaum},
journal= {arXiv preprint arXiv:2410.19979},
year = {2025}
}
Comments
31 pages, 0 figures; updated references, minor revisions