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March 2018 Growth exponent for loop-erased random walk in three dimensions
Daisuke Shiraishi
Ann. Probab. 46(2): 687-774 (March 2018). DOI: 10.1214/16-AOP1165

Abstract

Let $M_{n}$ be the number of steps of the loop-erasure of a simple random walk on $\mathbb{Z}^{3}$ run until its first exit from a ball of radius $n$. In the paper, we will show the existence of the growth exponent, that is, we show that there exists $\beta>0$ such that \begin{equation*}\lim_{n\to\infty}\frac{\log E(M_{n})}{\log n}=\beta.\end{equation*}

Citation

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Daisuke Shiraishi. "Growth exponent for loop-erased random walk in three dimensions." Ann. Probab. 46 (2) 687 - 774, March 2018. https://doi.org/10.1214/16-AOP1165

Information

Received: 1 July 2014; Revised: 1 November 2016; Published: March 2018
First available in Project Euclid: 9 March 2018

zbMATH: 06864072
MathSciNet: MR3773373
Digital Object Identifier: 10.1214/16-AOP1165

Subjects:
Primary: 60D05, 60G17, 60K35

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 2 • March 2018
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