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November 2005 Harmonic explorer and its convergence to SLE4
Oded Schramm, Scott Sheffield
Ann. Probab. 33(6): 2127-2148 (November 2005). DOI: 10.1214/009117905000000477

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.

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Oded Schramm. Scott Sheffield. "Harmonic explorer and its convergence to SLE4." Ann. Probab. 33 (6) 2127 - 2148, November 2005. https://doi.org/10.1214/009117905000000477

Information

Published: November 2005
First available in Project Euclid: 7 December 2005

zbMATH: 1095.60007
MathSciNet: MR2184093
Digital Object Identifier: 10.1214/009117905000000477

Subjects:
Primary: 60D05
Secondary: 82B43

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 6 • November 2005
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