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

The theory of the two-dimensional Liouville Quantum Gravity, first introduced by Polyakov in his 1981 work has become a key notion study random surfaces. In series articles, David, Huang, Kupiainen, Rhodes and Vargas, on one hand, Duplantier, Miller Sheffield other investigated this topic realm probability theory, both provided definitions for fundamentals objects theory: unit area quantum sphere boundary length disk. recent article, Aru, Huang Sun showed that given case coincide. We here two different perspectives disk show they define same probabilistic considering similar limiting procedures giving rise to them.