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'egory Marc Miermont},
  journal={Canadian Journal of Mathematics},
  year={2017},
  volume={71},
  pages={1-43}
}
  • Olivier Bernardi, Nicolas Curien, Gr'egory Marc Miermont
  • Published 2017
  • Mathematics
  • Canadian Journal of Mathematics
  • 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 geometry of the… CONTINUE READING

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