Escape regimes of biased random walks on Galton-Watson trees

• 成果类型: Article
• 署名作者: Bowditch, Adam
• 署名单位: University of Warwick
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0768-y
• 发表日期: 2018
• 页码: 685-768
• 关键词: behavior; LAW

摘要

We study biased random walk on subcritical and supercritical Galton-Watson trees conditioned to survive in the transient, sub-ballistic regime. By considering offspring laws with infinite variance, we extend previously known results for the walk on the supercritical tree and observe new trapping phenomena for the walk on the subcritical tree which, in this case, always yield sub-ballisticity. This is contrary to the walk on the supercritical tree which always has some ballistic phase.