The Annals of Probability

Harmonic explorer and its convergence to SLE4

Oded Schramm and Scott Sheffield

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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.

Article information

Source
Ann. Probab., Volume 33, Number 6 (2005), 2127-2148.

Dates
First available in Project Euclid: 7 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1133965855

Digital Object Identifier
doi:10.1214/009117905000000477

Mathematical Reviews number (MathSciNet)
MR2184093

Zentralblatt MATH identifier
1095.60007

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 82B43: Percolation [See also 60K35]

Keywords
SLE SLE_4 scaling limit harmonic explorer

Citation

Schramm, Oded; Sheffield, Scott. Harmonic explorer and its convergence to SLE 4. Ann. Probab. 33 (2005), no. 6, 2127--2148. doi:10.1214/009117905000000477. https://projecteuclid.org/euclid.aop/1133965855


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