Date
Mon, 22 May 2017
Time
14:15 - 15:15
Location
L3
Speaker
JASON MILLER
Organisation
University of Cambridge

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 (equivalently, a Liouville quantum gravity surface).  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.  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.  Joint work with E. Gwynne.

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