CONVERGENCE OF PERCOLATION ON UNIFORM QUADRANGULATIONS WITH BOUNDARY TO SLE6 ON √8/3-LIOUVILLE QUANTUM GRAVITY

Let Q be a free Boltzmann quadrangulation with simple boundary decorated by a critical (p = 3/4) face percolation configuration. We prove that the chordal percolation exploration path on Q between two marked boundary edges converges in the scaling limit to chordal SLE6 on an independent root 8/3-Liouville quantum gravity disk (equivalently, a Brownian disk). The topology of convergence is the Gromov-Hausdorff-Prokhorov-uniform topology, the natural analog of the Gromov-Hausdorff topology for curve-decorated metric measure spaces. We also obtain analogous scaling limit results for face percolation on the uniform infinite half-plane quadrangulation with simple boundary, and for site percolation on a uniform triangulation with simple boundary. Our method of proof is robust and, up to certain technical steps, extends to any percolation model on a random planar map which can be explored via peeling.