Harmonic explorer and its convergence to SLE 4

Abstract

The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left-hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE4 as the grid gets finer. © Institute of Mathematical Statistics, 2005.