The distribution of Gaussian multiplicative chaos on the unit interval

@article{Remy2020TheDO,
  title={The distribution of Gaussian multiplicative chaos on the unit interval},
  author={Guillaume Remy and Tunan Zhu},
  journal={The Annals of Probability},
  year={2020}
}
  • G. Remy, T. Zhu
  • Published 9 April 2018
  • Mathematics
  • The Annals of Probability
We consider the sub-critical Gaussian multiplicative chaos (GMC) measure defined on the unit interval [0,1] and prove an exact formula for the fractional moments of the total mass of this measure. Our formula includes the case where log-singularities (also called insertion points) are added in 0 and 1, the most general case predicted by the Selberg integral. The idea to perform this computation is to introduce certain auxiliary functions resembling holomorphic observables of conformal field… 

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