Transience of percolation clusters on wedges

Omer Angel; Itai Benjamini; Noam Berger; Yuval Peres

doi:10.1214/EJP.v11-345

Transience of percolation clusters on wedges

Omer Angel
, Itai Benjamini
, Noam Berger
, Yuval Peres

University of British Columbia
Weizmann Institute of Science Israel
University of California at Los Angeles
University of California at Berkeley

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We study random walks on supercritical percolation clusters on wedges in ℤ³, and show that the infinite percolation cluster is (a.s.) transient whenever the wedge is transient. This solves a question raised by O. Häggström and E. Mossel. We also show that for convex gauge functions satisfying a mild regularity condition, the existence of a finite energy flow on Z² is equivalent to the (a.s.) existence of a finite energy flow on the supercritical percolation cluster. This answers a question of C. Hoffman.

Original language	English
Pages (from-to)	655-669
Number of pages	15
Journal	Electronic Journal of Probability
Volume	11
DOIs	https://doi.org/10.1214/EJP.v11-345
State	Published - 1 Jan 2006
Externally published	Yes

Keywords

Percolation
Transience
Wedges

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abstract = "We study random walks on supercritical percolation clusters on wedges in ℤ3, and show that the infinite percolation cluster is (a.s.) transient whenever the wedge is transient. This solves a question raised by O. H{\"a}ggstr{\"o}m and E. Mossel. We also show that for convex gauge functions satisfying a mild regularity condition, the existence of a finite energy flow on Z2 is equivalent to the (a.s.) existence of a finite energy flow on the supercritical percolation cluster. This answers a question of C. Hoffman.",

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AU - Benjamini, Itai

AU - Berger, Noam

AU - Peres, Yuval

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N2 - We study random walks on supercritical percolation clusters on wedges in ℤ3, and show that the infinite percolation cluster is (a.s.) transient whenever the wedge is transient. This solves a question raised by O. Häggström and E. Mossel. We also show that for convex gauge functions satisfying a mild regularity condition, the existence of a finite energy flow on Z2 is equivalent to the (a.s.) existence of a finite energy flow on the supercritical percolation cluster. This answers a question of C. Hoffman.

AB - We study random walks on supercritical percolation clusters on wedges in ℤ3, and show that the infinite percolation cluster is (a.s.) transient whenever the wedge is transient. This solves a question raised by O. Häggström and E. Mossel. We also show that for convex gauge functions satisfying a mild regularity condition, the existence of a finite energy flow on Z2 is equivalent to the (a.s.) existence of a finite energy flow on the supercritical percolation cluster. This answers a question of C. Hoffman.

KW - Percolation

KW - Transience

KW - Wedges

UR - https://www.scopus.com/pages/publications/33746925194

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DO - 10.1214/EJP.v11-345

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VL - 11

SP - 655

EP - 669

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

ER -

Transience of percolation clusters on wedges

Abstract

Keywords

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