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2006 The Laplacian-$b$ random walk and the Schramm-Loewner evolution
Gregory F. Lawler
Illinois J. Math. 50(1-4): 701-746 (2006). DOI: 10.1215/ijm/1258059489

Abstract

The Laplacian-$b$ random walk is a measure on self-avoiding paths that at each step has translation probabilities weighted by the $b$th power of the probability that a simple random walk avoids the path up to that point. We give a heuristic argument as to what the scaling limit should be and call this process the Laplacian-$b$ motion, $LM_b$. In simply connected domains, this process is the Schramm-Loewner evolution with parameter $\kappa = 6/(2b+1)$. In non-simply connected domains, it corresponds to the harmonic random Loewner chains as introduced by Zhan.

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Gregory F. Lawler. "The Laplacian-$b$ random walk and the Schramm-Loewner evolution." Illinois J. Math. 50 (1-4) 701 - 746, 2006. https://doi.org/10.1215/ijm/1258059489

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1128.60069
MathSciNet: MR2247843
Digital Object Identifier: 10.1215/ijm/1258059489

Subjects:
Primary: 60J65
Secondary: 82B41

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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