Sharp threshold for percolation on expanders

Itai Benjamini; Stéphane Boucheron; Gábor Lugosi; Raphaël Rossignol

doi:10.1214/10-AOP610

Sharp threshold for percolation on expanders

Itai Benjamini, Stéphane Boucheron, Gábor Lugosi, Raphaël Rossignol

Department of Mathematics

Weizmann Institute of Science

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

Abstract

We study the appearance of the giant component in random subgraphs of a given large finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c ∈ ]0, 1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.

Original language	English
Pages (from-to)	130-145
Number of pages	16
Journal	Annals of Probability
Volume	40
Issue number	1
DOIs	https://doi.org/10.1214/10-AOP610
State	Published - Jan 2012

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/10-AOP610

Cite this

@article{a925f498bf00426eb371a290052e2e32,

title = "Sharp threshold for percolation on expanders",

abstract = "We study the appearance of the giant component in random subgraphs of a given large finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c ∈ ]0, 1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.",

author = "Itai Benjamini and St{\'e}phane Boucheron and G{\'a}bor Lugosi and Rapha{\"e}l Rossignol",

year = "2012",

month = jan,

doi = "10.1214/10-AOP610",

language = "الإنجليزيّة",

volume = "40",

pages = "130--145",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "1",

}

TY - JOUR

T1 - Sharp threshold for percolation on expanders

AU - Benjamini, Itai

AU - Boucheron, Stéphane

AU - Lugosi, Gábor

AU - Rossignol, Raphaël

PY - 2012/1

Y1 - 2012/1

N2 - We study the appearance of the giant component in random subgraphs of a given large finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c ∈ ]0, 1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.

AB - We study the appearance of the giant component in random subgraphs of a given large finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c ∈ ]0, 1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.

UR - http://www.scopus.com/inward/record.url?scp=84865105168&partnerID=8YFLogxK

U2 - 10.1214/10-AOP610

DO - 10.1214/10-AOP610

M3 - مقالة

SN - 0091-1798

VL - 40

SP - 130

EP - 145

JO - Annals of Probability

JF - Annals of Probability

IS - 1

ER -

Sharp threshold for percolation on expanders

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this