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

• Maury Bramson ^[1] ; Ofer Zeitouni ^[2] ; Martin P. W. Zerner ^[3]
  1. [1] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
  2. [2] Technion – Israel Institute of Technology

     Technion – Israel Institute of Technology

     Israel

     
  3. [3] Universität Tübingen

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 34, Nº. 3, 2006, págs. 821-856
• Idioma: inglés
• DOI: 10.1214/009117905000000783
• Texto completo no disponible (Saber más ...)
• Resumen

  • We construct forests that span ℤd, 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 ℤd, for which the corresponding random walk disobeys a certain zero–one law for directional transience.