A support theorem for exponential metrics of log-correlated Gaussian fields in arbitrary dimension

Andres A. Contreras Hip, Ewain Gwynne

Let $h$ be a log-correlated Gaussian field on ${\mathbb{R}}^d$, let $\gamma \in (0,\sqrt{2d}),$ let ${\mu }_h$ be the $\gamma$-Gaussian multiplicative chaos measure, and let $D_h$ be an exponential metric a…