CONTINUOUS-TIME WEAKLY SELF-AVOIDING WALK ON Z HAS STRICTLY MONOTONE ESCAPE SPEED

• 成果类型: Article
• 署名作者: Liu, Yucheng
• 署名单位: University of British Columbia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2098
• 发表日期: 2024
• 页码: 5522-5555
• 关键词: expansion; THEOREM

摘要

Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On Z, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing. The proof uses a transfer matrix method implemented via a supersymmetric version of the BFS-Dynkin isomorphism theorem, spectral theory, Tauberian theory, and stochastic dominance.