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arXiv · 2410.19979

Absolute continuity of non-Gaussian and Gaussian multiplicative chaos measures

Yujin H. Kim·Xaver Kriechbaum
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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.

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Yujin H. Kim, Xaver Kriechbaum. 2024-10-25. Absolute continuity of non-Gaussian and Gaussian multiplicative chaos measures. https://arxiv.org/abs/2410.19979

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