Shortest spanning trees and a counterexample for random walks in random environments

Maury D Bramson, Ofer Zeitouni, Martin P.W. Zerner

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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 languageEnglish (US)
Pages (from-to)821-856
Number of pages36
JournalAnnals of Probability
Volume34
Issue number3
DOIs
StatePublished - May 2006

Keywords

  • Random environment
  • Random walk
  • Spanning tree
  • Zero-one law

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