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2019 One-point function estimates for loop-erased random walk in three dimensions
Xinyi Li, Daisuke Shiraishi
Electron. J. Probab. 24: 1-46 (2019). DOI: 10.1214/19-EJP361

Abstract

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.

Citation

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Xinyi Li. Daisuke Shiraishi. "One-point function estimates for loop-erased random walk in three dimensions." Electron. J. Probab. 24 1 - 46, 2019. https://doi.org/10.1214/19-EJP361

Information

Received: 27 July 2018; Accepted: 8 September 2019; Published: 2019
First available in Project Euclid: 9 October 2019

zbMATH: 07142905
MathSciNet: MR4017129
Digital Object Identifier: 10.1214/19-EJP361

Subjects:
Primary: 82B41, 82C41

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