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2019 Transition probabilities for infinite two-sided loop-erased random walks
Christian Beneš, Gregory F. Lawler, Fredrik Viklund
Electron. J. Probab. 24: 1-22 (2019). DOI: 10.1214/19-EJP376


The infinite two-sided loop-erased random walk (LERW) is a measure on infinite self-avoiding walks that can be viewed as giving the law of the “middle part” of an infinite LERW loop going through $0$ and $\infty $. In this note we derive expressions for transition probabilities for this model in dimensions $d \ge 2$. For $d=2$ the formula can be further expressed in terms of a Laplacian with signed weights acting on certain discrete harmonic functions at the tips of the walk, and taking a determinant. The discrete harmonic functions are closely related to a discrete version of $z \mapsto \sqrt{z} $.


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Christian Beneš. Gregory F. Lawler. Fredrik Viklund. "Transition probabilities for infinite two-sided loop-erased random walks." Electron. J. Probab. 24 1 - 22, 2019.


Received: 18 January 2019; Accepted: 16 October 2019; Published: 2019
First available in Project Euclid: 4 December 2019

zbMATH: 07142933
MathSciNet: MR4040999
Digital Object Identifier: 10.1214/19-EJP376

Primary: 60G99, 82B41


Vol.24 • 2019
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