Shortest Spanning Trees and a Counterexample for Random Walks in Random Environments

We construct forests that span${\Bbb Z}^{d}$, 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...

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