A Boltzmann Approach to Percolation on Random Triangulations

@article{Bernardi2017ABA,
  title={A Boltzmann Approach to Percolation on Random Triangulations},
  author={Olivier Bernardi and Nicolas Curien and Gr{\'e}gory Miermont},
  journal={Canadian Journal of Mathematics},
  year={2017},
  volume={71},
  pages={1 - 43}
}
Abstract We study the percolation model on Boltzmann triangulations using a generating function approach. More precisely, we consider a Boltzmann model on the set of finite planar triangulations, together with a percolation configuration (either site-percolation or bond-percolation) on this triangulation. By enumerating triangulations with boundaries according to both the boundary length and the number of vertices/edges on the boundary, we are able to identify a phase transition for the… 

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