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

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

Access to Document

10.1214/EJP.v11-345

Cite this

@article{9857a8fee1f04f608fad754f44da7fba,

title = "Transience of percolation clusters on wedges",

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.",

keywords = "Percolation, Transience, Wedges",

author = "Omer Angel and Itai Benjamini and Noam Berger and Yuval Peres",

year = "2006",

month = jan,

day = "1",

doi = "10.1214/EJP.v11-345",

language = "English",

volume = "11",

pages = "655--669",

journal = "Electronic Journal of Probability",

issn = "1083-6489",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Transience of percolation clusters on wedges

AU - Angel, Omer

AU - Benjamini, Itai

AU - Berger, Noam

AU - Peres, Yuval

PY - 2006/1/1

Y1 - 2006/1/1

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 - http://www.scopus.com/inward/record.url?scp=33746925194&partnerID=8YFLogxK

U2 - 10.1214/EJP.v11-345

DO - 10.1214/EJP.v11-345

M3 - Article

AN - SCOPUS:33746925194

SN - 1083-6489

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

Access to Document

Other files and links

Fingerprint

Cite this