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Tail universality of critical Gaussian multiplicative chaos

Probability 2019-12-06 v1

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.

Keywords

Cite

@article{arxiv.1912.02755,
  title  = {Tail universality of critical Gaussian multiplicative chaos},
  author = {Mo Dick Wong},
  journal= {arXiv preprint arXiv:1912.02755},
  year   = {2019}
}