Tightness of exponential metrics for log-correlated Gaussian fields in arbitrary dimension

Jian Ding, Ewain Gwynne, Zijie Zhuang

We prove the tightness of a natural approximation scheme for an analog of the Liouville quantum gravity metric on ${\mathbb{R}}^d$ for arbitrary $d\ge 2$. More precisely, let $\{h_n\…