Negative moments for Gaussian multiplicative chaos on fractal sets

@article{Garban2018NegativeMF,
  title={Negative moments for Gaussian multiplicative chaos on fractal sets},
  author={Christophe Garban and Nina Holden and Avelio Sep'ulveda and Xin Sun},
  journal={arXiv: Probability},
  year={2018}
}
The objective of this note is to study the probability that the total mass of a sub-critical Gaussian multiplicative chaos (GMC) with arbitrary base measure $\sigma$ is small. When $\sigma$ has some continuous density w.r.t Lebesgue measure, a scaling argument shows that the logarithm of the total GMC mass is sub-Gaussian near $-\infty$. However, when $\sigma$ has no scaling properties, the situation is much less clear. In this paper, we prove that for any base measure $\sigma$, the total GMC… 
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