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

2012/03/02 by Croydon, David
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1203.0405

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 (d ≥ 5). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect occurs as soon 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.

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