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The rate of convergence of harmonic explorer to SLE4

Using the estimate of the difference between the discrete harmonic function and its corresponding continuous version we derive a rate of convergence of the Loewner driving function for the harmonic explorer to the Brownian motion with speed 4 on the real line. Based on this convergence rate, the derivative estimate for chordal $\mbox{SLE}_4$, and the estimate of tip structure modulus for harmonic explorer paths, we obtain an explicit power-law rate of convergence of the harmonic explorer paths to the trace of chordal $\mbox{SLE}_4$ in the supremum distance.

preprint2020arXivOpen access
Shi-Yi LanJin MaWang Zhou
math.CVmath.PR
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Shi-Yi LanJin MaWang Zhou

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