The harmonic explorer and its convergence to SLE(4)

Details The harmonic explorer and its convergence to SLE(4) The harmonic explorer and its convergence to SLE(4)

2003-10-15

arxiv.org/abs/math/0310210v3

AnnalsProbab.33:2127-2148,2005

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117905000000477 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117905000000477

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
SLE(4) as the grid gets finer.

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