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arXiv · 2003.01949

The rate of convergence of harmonic explorer to SLE4

Shi-Yi Lan·Jin Ma·Wang Zhou
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Abstract

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.

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Shi-Yi Lan, Jin Ma, Wang Zhou. 2020-03-04. The rate of convergence of harmonic explorer to SLE4. https://arxiv.org/abs/2003.01949

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