Unit boundary length quantum disk: a study of two different perspectives and their equivalence

@article{Cercle2019UnitBL,
  title={Unit boundary length quantum disk: a study of two different perspectives and their equivalence},
  author={Baptiste Cercl'e},
  journal={arXiv: Probability},
  year={2019}
}
The theory of the 2-dimensional Liouville Quantum Gravity, first introduced by Polyakov in his 1981 work has become a key notion in the study of random surfaces. In a series of articles, David, Huang, Kupiainen, Rhodes and Vargas, on the one hand, and Duplantier, Miller and Sheffield on the other hand, investigated this topic in the realm of probability theory, and both provided definitions for fundamentals objects of the theory: the unit area quantum sphere and the unit boundary length quantum… 

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Liouville quantum gravity surfaces with boundary as matings of trees

  • M. AngEwain Gwynne
  • Physics, Mathematics
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
  • 2021
For $\gamma \in (0,2)$, the quantum disk and $\gamma$-quantum wedge are two of the most natural types of Liouville quantum gravity (LQG) surfaces with boundary. These surfaces arise as scaling limits

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