FOUR-DIMENSIONAL LOOP-ERASED RANDOM WALK

• 成果类型: Article
• 署名作者: Lawler, Gregory; Sun, Xin; Wu, Wei
• 署名单位: University of Chicago; Columbia University; University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1349
• 发表日期: 2019
• 页码: 3866-3910
• 关键词: FIELDS

摘要

The loop-erased random walk (LERW) in Z(4) is the process obtained by erasing loops chronologically for a simple random walk. We prove that the escape probability of the LERW renormalized by (log n) 1/3 converges almost surely and in L-p for all p > 0. Along the way, we extend previous results by the first author building on slowly recurrent sets. We provide two applications for the escape probability. We construct the two-sided LERW, and we construct a +/- 1 spin model coupled with the wired spanning forests on Z(4) with the bi-Laplacian Gaussian field on R-4 as its scaling limit.