The rate of convergence of harmonic explorer to SLE4
Probability
2020-03-23 v2 Complex Variables
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 , 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 in the supremum distance.
Keywords
Cite
@article{arxiv.2003.01949,
title = {The rate of convergence of harmonic explorer to SLE4},
author = {Shi-Yi Lan and Jin Ma and Wang Zhou},
journal= {arXiv preprint arXiv:2003.01949},
year = {2020}
}
Comments
32 pages. A minor revision