Percolation on random triangulations and stable looptrees

We study site percolation on Angel & Schramm's uniform infinite planar triangulation. We compute several critical and near-critical exponents, and describe the scaling limit of the boundary of large percolation clusters in all regimes (subcritical, critical and supercritical). We prove in particular that the scaling limit of the boundary of large critical percolation clusters is the random stable looptree of index 3/2, which was introduced in a companion paper. We also give a conjecture linking looptrees of any index in (1,2) with scaling limits of cluster boundaries in random triangulations decorated with O(N) models.