We study critical site percolation on the uniform infinite half-planar triangulation with white–black boundary conditions. Previous work has established the convergence of percolation interface-decorated maps to SLE$_6$-decorated $\sqrt{8/3}$-Liouville quantum gravity surfaces, under the local GHPU topology.
In this work, we prove the convergence of the loop-erasure of the percolation interface and discuss how this limit may be identified. We will also mention a parallel result showing that the loop-erasure of the space-filling percolation interface on the UIPT converges to the 0-angle flow line.
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