Percolations on random maps I: Half-plane models

  title={Percolations on random maps I: Half-plane models},
  author={Omer Angel and Nicolas Curien},
  journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques},
  • Omer AngelN. Curien
  • Published 22 January 2013
  • Mathematics
  • Annales De L Institut Henri Poincare-probabilites Et Statistiques
We study Bernoulli percolations on random lattices of the half-plane obtained as local limit of uniform planar triangulations or quadrangulations. Using the characteristic spatial Markov property or peeling process [5] of these random lattices we prove a surprisingly simple universal formula for the critical threshold for bond and face percolations on these graphs. Our techniques also permit us to compute off-critical and critical exponents related to percolation clusters such as the volume and… 

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