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.
Original language | English (US) |
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Pages (from-to) | 1-19 |
Number of pages | 19 |
Journal | Journal of Statistical Physics |
Volume | 177 |
Issue number | 1 |
DOIs | |
State | Published - Oct 1 2019 |
Keywords
- Loop-erased
- Percolation
- SLE
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics