The Fyodorov–Bouchaud formula and Liouville conformal field theory

@article{Remy2020TheFF,
  title={The Fyodorov–Bouchaud formula and Liouville conformal field theory},
  author={Guillaume Remy},
  journal={Duke Mathematical Journal},
  year={2020}
}
  • G. Remy
  • Published 18 October 2017
  • Mathematics
  • Duke Mathematical Journal
In a remarkable paper in 2008, Fyodorov and Bouchaud conjectured an exact formula for the density of the total mass of (sub-critical) Gaussian multiplicative chaos (GMC) associated to the Gaussian free field (GFF) on the unit circle. In this paper we will give a proof of this formula. In the mathematical literature this is the first occurrence of an explicit probability density for the total mass of a GMC measure. The key observation of our proof is that the negative moments of the total mass… 

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