Croydon, David A. (2013) Slow movement of a random walk on the range of a random walk in the presence of an external field. Probability Theory and Related Fields, Volume 157 (Number 3-4). pp. 515-534. doi:10.1007/s00440-012-0463-y

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Abstract

In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (d5). 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Random walks (Mathematics), Localization theory
Journal or Publication Title:	Probability Theory and Related Fields
Publisher:	Springer
ISSN:	0178-8051
Official Date:	December 2013
Dates:	Date Event December 2013 Published
Date of first compliant deposit:	23 December 2015
Volume:	Volume 157
Number:	Number 3-4
Page Range:	pp. 515-534
DOI:	10.1007/s00440-012-0463-y
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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