Shortest Spanning Trees and a Counterexample for Random Walks in Random Environments

We construct forests that span${\Bbb Z}^{d}$, 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...

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Veröffentlicht in:	The Annals of probability 2006-05, Vol.34 (3), p.821-856
Hauptverfasser:	Bramson, Maury, Zeitouni, Ofer, Zerner, Martin P. W.
Format:	Artikel
Sprache:	eng
Schlagworte:	05C80 60K37 82D30 Decision trees Ellipticity Insulation Mathematical functions Mathematical models Polynomials Probabilities random environment Random variables Random walk spanning tree Studies Trees Umbrellas Vertices zero–one law
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container_title	The Annals of probability
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creator	Bramson, Maury Zeitouni, Ofer Zerner, Martin P. W.
description	We construct forests that span${\Bbb Z}^{d}$, 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${\Bbb Z}^{d}$, for which the corresponding random walk disobeys a certain zero-one law for directional transience.
doi_str_mv	10.1214/009117905000000783
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subjects	05C80 60K37 82D30 Decision trees Ellipticity Insulation Mathematical functions Mathematical models Polynomials Probabilities random environment Random variables Random walk spanning tree Studies Trees Umbrellas Vertices zero–one law
title	Shortest Spanning Trees and a Counterexample for Random Walks in Random Environments
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