Electronic Journal of Probability
- Electron. J. Probab.
- Volume 24 (2019), paper no. 111, 46 pp.
One-point function estimates for loop-erased random walk in three dimensions
In this work, we consider the loop-erased random walk (LERW) in three dimensions and give asymptotic estimates for the one-point function of LERW and the non-intersection probability of LERW and simple random walk for dyadic scales. These estimates will be crucial to the characterization of the convergence of LERW to its scaling limit in natural parametrization. As a step in the proof, we also obtain a coupling of two pairs of LERW and SRW with different starting points conditioned to avoid each other.
Electron. J. Probab., Volume 24 (2019), paper no. 111, 46 pp.
Received: 27 July 2018
Accepted: 8 September 2019
First available in Project Euclid: 9 October 2019
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loop-erased random walk
Li, Xinyi; Shiraishi, Daisuke. One-point function estimates for loop-erased random walk in three dimensions. Electron. J. Probab. 24 (2019), paper no. 111, 46 pp. doi:10.1214/19-EJP361. https://projecteuclid.org/euclid.ejp/1570586691