Slow movement of a random walk on the range of a random walk in the presence of an external field

• 成果类型: Article
• 署名作者: Croydon, David A.
• 署名单位: University of Warwick
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0463-y
• 发表日期: 2013
• 页码: 515-534
• 关键词: galton-watson trees; biased random-walks; random environment

摘要

In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect occurs as soon as a non-trivial bias is introduced. The proof applies a decomposition of the underlying simple random walk path at its cut-times to relate the associated biased random walk to a one-dimensional random walk in a random environment in Sinai's regime. Via this approach, a corresponding aging result is also proved.