Open Access
May 2006 Shortest spanning trees and a counterexample for random walks in random environments
Maury Bramson, Ofer Zeitouni, Martin P. W. Zerner
Ann. Probab. 34(3): 821-856 (May 2006). DOI: 10.1214/009117905000000783


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.


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Maury Bramson. Ofer Zeitouni. Martin P. W. Zerner. "Shortest spanning trees and a counterexample for random walks in random environments." Ann. Probab. 34 (3) 821 - 856, May 2006.


Published: May 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1102.60091
MathSciNet: MR2243869
Digital Object Identifier: 10.1214/009117905000000783

Primary: 60K37
Secondary: 05C80 , 82D30

Keywords: random environment , Random walk , spanning tree , Zero–one law

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 3 • May 2006
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