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

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dc.creatorBramson, Maury
dc.creatorZeitouni, Ofer
dc.creatorZerner, Martin P. W.
dc.date2005-01-29
dc.date2006-06-28
dc.date.accessioned2026-07-07T06:39:22Z
dc.date.available2026-07-07T06:39:22Z
dc.descriptionWe construct forests that span $\mathbb{Z}^d$, $d\geq2$, 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 $d\geq3$, two independent copies of such forests, pointing in opposite directions, can be pruned so as to become disjoint. From this, we construct in $d\geq3$ a stationary, polynomially mixing and uniformly elliptic environment of nearest-neighbor transition probabilities on $\mathbb{Z}^d$, for which the corresponding random walk disobeys a certain zero--one law for directional transience.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117905000000783 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0501533
dc.identifierhttp://arxiv.org/abs/math/0501533
dc.identifierAnnals of Probability 2006, Vol. 34, No. 3, 821-856
dc.identifierdoi:10.1214/009117905000000783
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101050
dc.subjectProbability
dc.subject60K37 (Primary) 05C80, 82D30 (Secondary)
dc.titleShortest spanning trees and a counterexample for random walks in random environments
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