Self-repelling walk on the Sierpiniski gasket

• 成果类型: Article
• 署名作者: Hambly, BM; Hattori, K; Hattori, T
• 署名单位: University of Oxford; Shinshu University; Nagoya University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400100192
• 发表日期: 2002
• 页码: 1-25
• 关键词: brownian-motion; large deviations; avoiding paths; bond repulsion; LIMIT-THEOREMS

摘要

We construct a one-parameter family of self-repelling processes on the Sierpinski gasket, by taking continuum limits of self-repelling walks on the pre-Sierpinski gaskets. We prove that our model interpolates between the Brownian motion and the self-avoiding process on the Sierpinski gasket. Namely, we prove that the process is continuous in the parameter in the sense of convergence in law, and that the order of Holder continuity of the sample paths is also continuous in the parameter. We also establish a law of the iterated logarithm for the self-repelling process. Finally we show that this approach yields a new class of one-dimensional self-repelling processes.