Concentration estimates for the isoperimetric constant of the supercritical percolation cluster

Eviatar B. Procaccia; Ron Rosenthal

doi:10.1214/ECP.v17-2185

Concentration estimates for the isoperimetric constant of the supercritical percolation cluster

Eviatar B. Procaccia, Ron Rosenthal

Department of Mathematics

Weizmann Institute of Science

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

Abstract

We consider the Cheeger constant φ(n) of the giant component of supercritical bond percolation on ℤ^d/nℤ^d. We show that the variance of φ(n) is bounded by ξ/n^d, where ξ is a positive constant that depends only on the dimension d and the percolation parameter.

Original language	English
Journal	Electronic Communications in Probability
Volume	17
DOIs	https://doi.org/10.1214/ECP.v17-2185
State	Published - 2012

Keywords

Concentration
Isoperimetric constant
Percolation

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/ECP.v17-2185

Cite this

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title = "Concentration estimates for the isoperimetric constant of the supercritical percolation cluster",

abstract = "We consider the Cheeger constant φ(n) of the giant component of supercritical bond percolation on ℤd/nℤd. We show that the variance of φ(n) is bounded by ξ/nd, where ξ is a positive constant that depends only on the dimension d and the percolation parameter.",

keywords = "Concentration, Isoperimetric constant, Percolation",

author = "Procaccia, \{Eviatar B.\} and Ron Rosenthal",

note = "ERC StG [239990]The authors would like to thank Itai Benjamini for suggesting the problem. We would also like to thank the detailed comments of an anonymous referee. The research of R.R was partially supported by ERC StG Number 239990",

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doi = "10.1214/ECP.v17-2185",

language = "الإنجليزيّة",

volume = "17",

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AU - Procaccia, Eviatar B.

AU - Rosenthal, Ron

N1 - ERC StG [239990]The authors would like to thank Itai Benjamini for suggesting the problem. We would also like to thank the detailed comments of an anonymous referee. The research of R.R was partially supported by ERC StG Number 239990

PY - 2012

Y1 - 2012

N2 - We consider the Cheeger constant φ(n) of the giant component of supercritical bond percolation on ℤd/nℤd. We show that the variance of φ(n) is bounded by ξ/nd, where ξ is a positive constant that depends only on the dimension d and the percolation parameter.

AB - We consider the Cheeger constant φ(n) of the giant component of supercritical bond percolation on ℤd/nℤd. We show that the variance of φ(n) is bounded by ξ/nd, where ξ is a positive constant that depends only on the dimension d and the percolation parameter.

KW - Concentration

KW - Isoperimetric constant

KW - Percolation

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U2 - 10.1214/ECP.v17-2185

DO - 10.1214/ECP.v17-2185

M3 - مقالة

SN - 1083-589X

VL - 17

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

Concentration estimates for the isoperimetric constant of the supercritical percolation cluster

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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