Percolations on random maps I: Half-plane models

@article{Angel2013PercolationsOR,
  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},
  year={2013},
  volume={51},
  pages={405-431}
}
  • 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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59 Citations
Highly Influential Citations
9
Background Citations
28
Methods Citations
19
Results Citations
1

59 Citations

Universal aspects of critical percolation on random half-planar maps

We study a large class of Bernoulli percolation models on random lattices of the half- plane, obtained as local limits of uniform planar triangulations or quadrangulations. We first compute the exact…

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Geometry and percolation on half planar triangulations

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On Site Percolation in Random Quadrangulations of the Half-Plane

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PERCOLATION ON UNIFORM INFINITE TRIANGULATIONS

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Percolation on uniform infinite planar maps

We construct the uniform infinite planar map (UIPM), obtained as the $n \to \infty$ local limit of planar maps with $n$ edges, chosen uniformly at random. We then describe how the UIPM can be sampled…
...

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