Conformal Invariance of the Loop-Erased Percolation Explorer

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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.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalJournal of Statistical Physics
Issue number1
StatePublished - Oct 1 2019


  • Loop-erased
  • Percolation
  • SLE

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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