Let Q be a uniformly random 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 SLE(6) on the Brownian disk. 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. Based on joint work with E. Gwynne.
Convergence of percolation on uniform quadrangulations
Jason Miller (Cambridge)
Wed, 29/11/2017 - 13:00
W316, Queen's Building