The (p,q)-moment of the bulk/boundary quotient of Gaussian multiplicative chaos is finite whenever p is below min(2/γ²+q/2, 4/γ²), and blows up at the 4/γ² boundary.
Tail universality of critical Gaussian multiplicative chaos
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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.
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Tail Profile of Bulk Gaussian Multiplicative Chaos Measures I: Bulk/Boundary Quotients
The (p,q)-moment of the bulk/boundary quotient of Gaussian multiplicative chaos is finite whenever p is below min(2/γ²+q/2, 4/γ²), and blows up at the 4/γ² boundary.