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arXiv · 1806.11561

Conformal invariance of the loop-erased percolation explorer

Tom Kennedy
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Abstract

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.

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Tom Kennedy. 2018-06-29. Conformal invariance of the loop-erased percolation explorer. https://doi.org/10.1007/s10955-019-02354-9

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