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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

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Official URL: http://dx.doi.org/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:
DateEvent
December 2013Published
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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