14 research outputs found
Slow movement of a random walk on the range of a random walk in the presence of an external field
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 \geq 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
Some remarks on the geometry of the Standard Map
We define and compute hyperbolic coordinates and associated foliations which
provide a new way to describe the geometry of the standard map. We also
identify a uniformly hyperbolic region and a complementary 'critical' region
containing a smooth curve of tangencies between certain canonical 'stable'
foliations.Comment: 25 pages, 11 figure