The geometry of a critical percolation cluster on the UIPT

Matthias Gorny (1) , Édouard Maurel-Segala (1) , Arvind Singh (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We consider a critical Bernoulli site percolation on the uniform infinite planar triangulation. We study the tail distributions of the peeling time, perimeter, and volume of the hull of a critical cluster. The exponents obtained here differs by a factor 2 from those computed previously by Angel and Curien (2015) in the case of critical site percolation on the uniform infinite half-plane triangulation.

Mots clés: random planar triangulation; critical exponents; percolation

Domaines: Probabilités [math.PR]

Matthias Gorny, Édouard Maurel-Segala, Arvind Singh. The geometry of a critical percolation cluster on the UIPT. 2017. ⟨hal-01427244⟩