Publication Date:
2012-10-30
Description:
In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions ( d ³ 5 ). 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. Content Type Journal Article Pages 1-20 DOI 10.1007/s00440-012-0463-y Authors David A. Croydon, Department of Statistics, University of Warwick, Coventry, CV4 7AL UK Journal Probability Theory and Related Fields Online ISSN 1432-2064 Print ISSN 0178-8051
Print ISSN:
0178-8051
Electronic ISSN:
1432-2064
Topics:
Mathematics
