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

• 成果类型: Article
• 署名作者: Bramson, Maury; Zeitouni, Ofer; Zerner, Martin P. W.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Technion Israel Institute of Technology; Technion Israel Institute of Technology; Eberhard Karls University of Tubingen; Stanford University; University of California System; University of California Davis
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000783
• 发表日期: 2006
• 页码: 821-856
• 关键词: zero-one law; large numbers

摘要

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.