Abstract
We construct forests that span ℤ d,d≥2, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For d ≥ 3, two independent copies of such forests, pointing in opposite directions, can be pruned so as to become disjoint. From this, we construct in d ≥ 3 a stationary, polynomially mixing and uniformly elliptic environment of nearest-neighbor transition probabilities on ℤ d, for which the corresponding random walk disobeys a certain zero-one law for directional transience.
Original language | English (US) |
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Pages (from-to) | 821-856 |
Number of pages | 36 |
Journal | Annals of Probability |
Volume | 34 |
Issue number | 3 |
DOIs | |
State | Published - May 2006 |
Keywords
- Random environment
- Random walk
- Spanning tree
- Zero-one law