Negative moments for gaussian multiplicative chaos on fractal sets

Christophe Garban, Nina Holden, Avelio Sepúlveda, Xin Sun

Research output: Contribution to journalArticlepeer-review


The objective of this note is to study the probability that the total mass of a subcritical Gaussian multiplicative chaos (GMC) with arbitrary base measure σ is small. When σ 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 −∞. However, when σ has no scaling properties, the situation is much less clear. In this paper, we prove that for any base measure σ, the total GMC mass has negative moments of all orders.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalElectronic Communications in Probability
StatePublished - 2018


  • Gaussian free field
  • Liouville measure
  • Log-correlated fields
  • Negative moments

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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