Tail universality of critical Gaussian multiplicative chaos

Abstract

In this article we study the tail probability of the mass of critical Gaussian multiplicative chaos (GMC) associated to a general class of log-correlated Gaussian fields in any dimension, including the Gaussian free field (GFF) in dimension two. More precisely, we derive a fully explicit formula for the leading order asymptotics for the tail probability and demonstrate a new universality phenomenon. Our analysis here shares similar philosophy with the subcritical case but requires a different approach due to complications in the analogous localisation step, and we also employ techniques from recent studies of fusion estimates in GMC theory.