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Slow movement of a random walk on the range of a random walk in the presence of an external field
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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 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-012-0463-y
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 | ||||
Date of first compliant deposit: | 23 December 2015 | ||||
Date of first compliant Open Access: | 23 December 2015 |
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