Harmonic explorer and its convergence to \(\text{SLE}_4\). (English) Zbl 1095.60007

The harmonic explorer is a new model similar in spirit to the loop erased random walk and diffusion limited aggregation. It is a random grid path in the planar honeycomb lattice that at each step of generation takes a turn to the right with probability equal to a discrete harmonic measure. The authors prove that the harmonic explorer converges to the chordal stochastic Loewner evolution with parameter 4 \(\text{(SLE}_4)\) as the hexagonal mesh gets finer.


60D05 Geometric probability and stochastic geometry
82B43 Percolation


scaling limit
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