Scaling limit of the recurrent biased random walk on a Galton-Watson tree

• 成果类型: Article
• 署名作者: Aidekon, Elie; de Raphelis, Loic
• 署名单位: Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0739-8
• 发表日期: 2017
• 页码: 643-666
• 关键词: continuum random tree; cookie random-walk; random environment; regular tree; percolation; GROWTH; speed

摘要

We show that the trace of the null recurrent biased random walk on a Galton-Watson tree properly renormalized converges to the Brownian forest. Our result extends to the setting of the random walk in random environment on a Galton-Watson tree.