One-point function estimates for loop-erased random walk in three dimensions

2018/07/02 by Xinyi Li, Li, Xinyi, Daisuke Shiraishi +1
Mathematics · Physics and Astronomy · #60K35 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.1807.00541

39 pages, 2 figures

arxiv created 2018/07/02 · openalex publication_date 2018/07/02 · arxiv updated 2018/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we consider loop-erased random walk (LERW) in three dimensions and give an asymptotic estimate on the one-point function for LERW and the non-intersection probability of LERW and simple random walk in three dimensions 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.

Related

• Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk
• Convergence of three-dimensional loop-erased random walk in the natural parametrization
• The scaling limit of loop-erased random walk in three dimensions
• Growth exponent for loop-erased random walk in three dimensions
• Capacity of loop-erased random walk