Transience of percolation clusters on wedges

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We study random walks on supercritical percolation clusters on wedges in $\Z^3$, and show that the infinite percolation cluster is (a.s.) transient whenever the wedge is transient. This solves a question raised by O. Haggstrom and E. Mossel. We also show that for convex gauge functions satisfying a mild regularity condition, the existence of a finite energy flow on $Z^2$ is equivalent to the (a.s.) existence of a finite energy flow on the supercritical percolation cluster. This solves a question of C. Hoffman.
17 pages

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Probability, 60J45; 60J15,60K35

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http://salesiana.dossiersoluciones.com/handle/123456789/64293

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206130
 http://arxiv.org/abs/math/0206130

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arXiv