Conformal Invariance of the Loop-Erased Percolation Explorer

We consider critical percolation on the triangular lattice in a bounded simply connected domain with boundary conditions that force an interface between two prescribed boundary points. We say the interface forms a “near-loop” when it comes within one lattice spacing of itself. We define a new curve by erasing these near-loops as we traverse the interface. Our Monte Carlo simulations of this model lead us to conclude that the scaling limit of this loop-erased percolation interface is conformally invariant and has fractal dimension 4 / 3. However, it is not SLE _{8 / 3}. We also consider the process in which a near-loop is when the explorer comes within two lattice spacings of itself.